Daily Papers

We study reinforcement learning with linear function approximation and adversarially changing cost functions, a setup that has mostly been considered under simplifying assumptions such as full information feedback or exploratory conditions.We present a computationally efficient policy optimization algorithm for the challenging general setting of unknown dynamics and bandit feedback, featuring a combination of mirror-descent and least squares policy evaluation in an auxiliary MDP used to compute exploration bonuses.Our algorithm obtains an widetilde O(K^{6/7}) regret bound, improving significantly over previous state-of-the-art of widetilde O (K^{14/15}) in this setting. In addition, we present a version of the same algorithm under the assumption a simulator of the environment is available to the learner (but otherwise no exploratory assumptions are made), and prove it obtains state-of-the-art regret of widetilde O (K^{2/3}).

Recently, there is an emerging interest in adversarially training a classifier with a rejection option (also known as a selective classifier) for boosting adversarial robustness. While rejection can incur a cost in many applications, existing studies typically associate zero cost with rejecting perturbed inputs, which can result in the rejection of numerous slightly-perturbed inputs that could be correctly classified. In this work, we study adversarially-robust classification with rejection in the stratified rejection setting, where the rejection cost is modeled by rejection loss functions monotonically non-increasing in the perturbation magnitude. We theoretically analyze the stratified rejection setting and propose a novel defense method -- Adversarial Training with Consistent Prediction-based Rejection (CPR) -- for building a robust selective classifier. Experiments on image datasets demonstrate that the proposed method significantly outperforms existing methods under strong adaptive attacks. For instance, on CIFAR-10, CPR reduces the total robust loss (for different rejection losses) by at least 7.3% under both seen and unseen attacks.

Cross-entropy is a widely used loss function in applications. It coincides with the logistic loss applied to the outputs of a neural network, when the softmax is used. But, what guarantees can we rely on when using cross-entropy as a surrogate loss? We present a theoretical analysis of a broad family of loss functions, comp-sum losses, that includes cross-entropy (or logistic loss), generalized cross-entropy, the mean absolute error and other cross-entropy-like loss functions. We give the first H-consistency bounds for these loss functions. These are non-asymptotic guarantees that upper bound the zero-one loss estimation error in terms of the estimation error of a surrogate loss, for the specific hypothesis set H used. We further show that our bounds are tight. These bounds depend on quantities called minimizability gaps. To make them more explicit, we give a specific analysis of these gaps for comp-sum losses. We also introduce a new family of loss functions, smooth adversarial comp-sum losses, that are derived from their comp-sum counterparts by adding in a related smooth term. We show that these loss functions are beneficial in the adversarial setting by proving that they admit H-consistency bounds. This leads to new adversarial robustness algorithms that consist of minimizing a regularized smooth adversarial comp-sum loss. While our main purpose is a theoretical analysis, we also present an extensive empirical analysis comparing comp-sum losses. We further report the results of a series of experiments demonstrating that our adversarial robustness algorithms outperform the current state-of-the-art, while also achieving a superior non-adversarial accuracy.

Despite incredible advances, deep learning has been shown to be susceptible to adversarial attacks. Numerous approaches have been proposed to train robust networks both empirically and certifiably. However, most of them defend against only a single type of attack, while recent work takes steps forward in defending against multiple attacks. In this paper, to understand multi-target robustness, we view this problem as a bargaining game in which different players (adversaries) negotiate to reach an agreement on a joint direction of parameter updating. We identify a phenomenon named player domination in the bargaining game, namely that the existing max-based approaches, such as MAX and MSD, do not converge. Based on our theoretical analysis, we design a novel framework that adjusts the budgets of different adversaries to avoid any player dominance. Experiments on standard benchmarks show that employing the proposed framework to the existing approaches significantly advances multi-target robustness.

This paper proposes a new loss function for adversarial training. Since adversarial training has difficulties, e.g., necessity of high model capacity, focusing on important data points by weighting cross-entropy loss has attracted much attention. However, they are vulnerable to sophisticated attacks, e.g., Auto-Attack. This paper experimentally reveals that the cause of their vulnerability is their small margins between logits for the true label and the other labels. Since neural networks classify the data points based on the logits, logit margins should be large enough to avoid flipping the largest logit by the attacks. Importance-aware methods do not increase logit margins of important samples but decrease those of less-important samples compared with cross-entropy loss. To increase logit margins of important samples, we propose switching one-vs-the-rest loss (SOVR), which switches from cross-entropy to one-vs-the-rest loss for important samples that have small logit margins. We prove that one-vs-the-rest loss increases logit margins two times larger than the weighted cross-entropy loss for a simple problem. We experimentally confirm that SOVR increases logit margins of important samples unlike existing methods and achieves better robustness against Auto-Attack than importance-aware methods.

Adversarial attacks in reinforcement learning (RL) often assume highly-privileged access to the victim's parameters, environment, or data. Instead, this paper proposes a novel adversarial setting called a Cheap Talk MDP in which an Adversary can merely append deterministic messages to the Victim's observation, resulting in a minimal range of influence. The Adversary cannot occlude ground truth, influence underlying environment dynamics or reward signals, introduce non-stationarity, add stochasticity, see the Victim's actions, or access their parameters. Additionally, we present a simple meta-learning algorithm called Adversarial Cheap Talk (ACT) to train Adversaries in this setting. We demonstrate that an Adversary trained with ACT still significantly influences the Victim's training and testing performance, despite the highly constrained setting. Affecting train-time performance reveals a new attack vector and provides insight into the success and failure modes of existing RL algorithms. More specifically, we show that an ACT Adversary is capable of harming performance by interfering with the learner's function approximation, or instead helping the Victim's performance by outputting useful features. Finally, we show that an ACT Adversary can manipulate messages during train-time to directly and arbitrarily control the Victim at test-time. Project video and code are available at https://sites.google.com/view/adversarial-cheap-talk

The dominant line of work in domain adaptation has focused on learning invariant representations using domain-adversarial training. In this paper, we interpret this approach from a game theoretical perspective. Defining optimal solutions in domain-adversarial training as a local Nash equilibrium, we show that gradient descent in domain-adversarial training can violate the asymptotic convergence guarantees of the optimizer, oftentimes hindering the transfer performance. Our analysis leads us to replace gradient descent with high-order ODE solvers (i.e., Runge-Kutta), for which we derive asymptotic convergence guarantees. This family of optimizers is significantly more stable and allows more aggressive learning rates, leading to high performance gains when used as a drop-in replacement over standard optimizers. Our experiments show that in conjunction with state-of-the-art domain-adversarial methods, we achieve up to 3.5% improvement with less than of half training iterations. Our optimizers are easy to implement, free of additional parameters, and can be plugged into any domain-adversarial framework.

Adversarial training is a widely used strategy for making neural networks resistant to adversarial perturbations. For a neural network of width m, n input training data in d dimension, it takes Omega(mnd) time cost per training iteration for the forward and backward computation. In this paper we analyze the convergence guarantee of adversarial training procedure on a two-layer neural network with shifted ReLU activation, and shows that only o(m) neurons will be activated for each input data per iteration. Furthermore, we develop an algorithm for adversarial training with time cost o(m n d) per iteration by applying half-space reporting data structure.

The loss functions of many learning problems contain multiple additive terms that can disagree and yield conflicting update directions. For Physics-Informed Neural Networks (PINNs), loss terms on initial/boundary conditions and physics equations are particularly interesting as they are well-established as highly difficult tasks. To improve learning the challenging multi-objective task posed by PINNs, we propose the ConFIG method, which provides conflict-free updates by ensuring a positive dot product between the final update and each loss-specific gradient. It also maintains consistent optimization rates for all loss terms and dynamically adjusts gradient magnitudes based on conflict levels. We additionally leverage momentum to accelerate optimizations by alternating the back-propagation of different loss terms. We provide a mathematical proof showing the convergence of the ConFIG method, and it is evaluated across a range of challenging PINN scenarios. ConFIG consistently shows superior performance and runtime compared to baseline methods. We also test the proposed method in a classic multi-task benchmark, where the ConFIG method likewise exhibits a highly promising performance. Source code is available at https://tum-pbs.github.io/ConFIG

This work proposes a procedure for designing algorithms for specific adaptive data collection tasks like active learning and pure-exploration multi-armed bandits. Unlike the design of traditional adaptive algorithms that rely on concentration of measure and careful analysis to justify the correctness and sample complexity of the procedure, our adaptive algorithm is learned via adversarial training over equivalence classes of problems derived from information theoretic lower bounds. In particular, a single adaptive learning algorithm is learned that competes with the best adaptive algorithm learned for each equivalence class. Our procedure takes as input just the available queries, set of hypotheses, loss function, and total query budget. This is in contrast to existing meta-learning work that learns an adaptive algorithm relative to an explicit, user-defined subset or prior distribution over problems which can be challenging to define and be mismatched to the instance encountered at test time. This work is particularly focused on the regime when the total query budget is very small, such as a few dozen, which is much smaller than those budgets typically considered by theoretically derived algorithms. We perform synthetic experiments to justify the stability and effectiveness of the training procedure, and then evaluate the method on tasks derived from real data including a noisy 20 Questions game and a joke recommendation task.

We study a version of adversarial classification where an adversary is empowered to corrupt data inputs up to some distance varepsilon, using tools from variational analysis. In particular, we describe necessary conditions associated with the optimal classifier subject to such an adversary. Using the necessary conditions, we derive a geometric evolution equation which can be used to track the change in classification boundaries as varepsilon varies. This evolution equation may be described as an uncoupled system of differential equations in one dimension, or as a mean curvature type equation in higher dimension. In one dimension, and under mild assumptions on the data distribution, we rigorously prove that one can use the initial value problem starting from varepsilon=0, which is simply the Bayes classifier, in order to solve for the global minimizer of the adversarial problem for small values of varepsilon. In higher dimensions we provide a similar result, albeit conditional to the existence of regular solutions of the initial value problem. In the process of proving our main results we obtain a result of independent interest connecting the original adversarial problem with an optimal transport problem under no assumptions on whether classes are balanced or not. Numerical examples illustrating these ideas are also presented.

It is not fully understood why adversarial examples can deceive neural networks and transfer between different networks. To elucidate this, several studies have hypothesized that adversarial perturbations, while appearing as noises, contain class features. This is supported by empirical evidence showing that networks trained on mislabeled adversarial examples can still generalize well to correctly labeled test samples. However, a theoretical understanding of how perturbations include class features and contribute to generalization is limited. In this study, we provide a theoretical framework for understanding learning from perturbations using a one-hidden-layer network trained on mutually orthogonal samples. Our results highlight that various adversarial perturbations, even perturbations of a few pixels, contain sufficient class features for generalization. Moreover, we reveal that the decision boundary when learning from perturbations matches that from standard samples except for specific regions under mild conditions. The code is available at https://github.com/s-kumano/learning-from-adversarial-perturbations.

The study of provable adversarial robustness for deep neural networks (DNNs) has mainly focused on static supervised learning tasks such as image classification. However, DNNs have been used extensively in real-world adaptive tasks such as reinforcement learning (RL), making such systems vulnerable to adversarial attacks as well. Prior works in provable robustness in RL seek to certify the behaviour of the victim policy at every time-step against a non-adaptive adversary using methods developed for the static setting. But in the real world, an RL adversary can infer the defense strategy used by the victim agent by observing the states, actions, etc., from previous time-steps and adapt itself to produce stronger attacks in future steps. We present an efficient procedure, designed specifically to defend against an adaptive RL adversary, that can directly certify the total reward without requiring the policy to be robust at each time-step. Our main theoretical contribution is to prove an adaptive version of the Neyman-Pearson Lemma -- a key lemma for smoothing-based certificates -- where the adversarial perturbation at a particular time can be a stochastic function of current and previous observations and states as well as previous actions. Building on this result, we propose policy smoothing where the agent adds a Gaussian noise to its observation at each time-step before passing it through the policy function. Our robustness certificates guarantee that the final total reward obtained by policy smoothing remains above a certain threshold, even though the actions at intermediate time-steps may change under the attack. Our experiments on various environments like Cartpole, Pong, Freeway and Mountain Car show that our method can yield meaningful robustness guarantees in practice.

In order to train networks for verified adversarial robustness, it is common to over-approximate the worst-case loss over perturbation regions, resulting in networks that attain verifiability at the expense of standard performance. As shown in recent work, better trade-offs between accuracy and robustness can be obtained by carefully coupling adversarial training with over-approximations. We hypothesize that the expressivity of a loss function, which we formalize as the ability to span a range of trade-offs between lower and upper bounds to the worst-case loss through a single parameter (the over-approximation coefficient), is key to attaining state-of-the-art performance. To support our hypothesis, we show that trivial expressive losses, obtained via convex combinations between adversarial attacks and IBP bounds, yield state-of-the-art results across a variety of settings in spite of their conceptual simplicity. We provide a detailed analysis of the relationship between the over-approximation coefficient and performance profiles across different expressive losses, showing that, while expressivity is essential, better approximations of the worst-case loss are not necessarily linked to superior robustness-accuracy trade-offs.

In value-based reinforcement learning methods such as deep Q-learning, function approximation errors are known to lead to overestimated value estimates and suboptimal policies. We show that this problem persists in an actor-critic setting and propose novel mechanisms to minimize its effects on both the actor and the critic. Our algorithm builds on Double Q-learning, by taking the minimum value between a pair of critics to limit overestimation. We draw the connection between target networks and overestimation bias, and suggest delaying policy updates to reduce per-update error and further improve performance. We evaluate our method on the suite of OpenAI gym tasks, outperforming the state of the art in every environment tested.

Adversarial robustness is a key desirable property of neural networks. It has been empirically shown to be affected by their sizes, with larger networks being typically more robust. Recently, Bubeck and Sellke proved a lower bound on the Lipschitz constant of functions that fit the training data in terms of their number of parameters. This raises an interesting open question, do -- and can -- functions with more parameters, but not necessarily more computational cost, have better robustness? We study this question for sparse Mixture of Expert models (MoEs), that make it possible to scale up the model size for a roughly constant computational cost. We theoretically show that under certain conditions on the routing and the structure of the data, MoEs can have significantly smaller Lipschitz constants than their dense counterparts. The robustness of MoEs can suffer when the highest weighted experts for an input implement sufficiently different functions. We next empirically evaluate the robustness of MoEs on ImageNet using adversarial attacks and show they are indeed more robust than dense models with the same computational cost. We make key observations showing the robustness of MoEs to the choice of experts, highlighting the redundancy of experts in models trained in practice.

One prominent approach toward resolving the adversarial vulnerability of deep neural networks is the two-player zero-sum paradigm of adversarial training, in which predictors are trained against adversarially chosen perturbations of data. Despite the promise of this approach, algorithms based on this paradigm have not engendered sufficient levels of robustness and suffer from pathological behavior like robust overfitting. To understand this shortcoming, we first show that the commonly used surrogate-based relaxation used in adversarial training algorithms voids all guarantees on the robustness of trained classifiers. The identification of this pitfall informs a novel non-zero-sum bilevel formulation of adversarial training, wherein each player optimizes a different objective function. Our formulation yields a simple algorithmic framework that matches and in some cases outperforms state-of-the-art attacks, attains comparable levels of robustness to standard adversarial training algorithms, and does not suffer from robust overfitting.

Reinforcement learning (RL) has advanced greatly in the past few years with the employment of effective deep neural networks (DNNs) on the policy networks. With the great effectiveness came serious vulnerability issues with DNNs that small adversarial perturbations on the input can change the output of the network. Several works have pointed out that learned agents with a DNN policy network can be manipulated against achieving the original task through a sequence of small perturbations on the input states. In this paper, we demonstrate furthermore that it is also possible to impose an arbitrary adversarial reward on the victim policy network through a sequence of attacks. Our method involves the latest adversarial attack technique, Adversarial Transformer Network (ATN), that learns to generate the attack and is easy to integrate into the policy network. As a result of our attack, the victim agent is misguided to optimise for the adversarial reward over time. Our results expose serious security threats for RL applications in safety-critical systems including drones, medical analysis, and self-driving cars.

Large language models (LLMs) are vulnerable to adversarial attacks that can bypass their safety guardrails. In many domains, adversarial training has proven to be one of the most promising methods to reliably improve robustness against such attacks. Yet, in the context of LLMs, current methods for adversarial training are hindered by the high computational costs required to perform discrete adversarial attacks at each training iteration. We address this problem by instead calculating adversarial attacks in the continuous embedding space of the LLM, which is orders of magnitudes more efficient. We propose a fast adversarial training algorithm (C-AdvUL) composed of two losses: the first makes the model robust on continuous embedding attacks computed on an adversarial behaviour dataset; the second ensures the usefulness of the final model by fine-tuning on utility data. Moreover, we introduce C-AdvIPO, an adversarial variant of IPO that does not require utility data for adversarially robust alignment. Our empirical evaluation on four models from different families (Gemma, Phi3, Mistral, Zephyr) and at different scales (2B, 3.8B, 7B) shows that both algorithms substantially enhance LLM robustness against discrete attacks (GCG, AutoDAN, PAIR), while maintaining utility. Our results demonstrate that robustness to continuous perturbations can extrapolate to discrete threat models. Thereby, we present a path toward scalable adversarial training algorithms for robustly aligning LLMs.

We study robustness to test-time adversarial attacks in the regression setting with ell_p losses and arbitrary perturbation sets. We address the question of which function classes are PAC learnable in this setting. We show that classes of finite fat-shattering dimension are learnable in both realizable and agnostic settings. Moreover, for convex function classes, they are even properly learnable. In contrast, some non-convex function classes provably require improper learning algorithms. Our main technique is based on a construction of an adversarially robust sample compression scheme of a size determined by the fat-shattering dimension. Along the way, we introduce a novel agnostic sample compression scheme for real-valued functions, which may be of independent interest.

The origin of adversarial examples is still inexplicable in research fields, and it arouses arguments from various viewpoints, albeit comprehensive investigations. In this paper, we propose a way of delving into the unexpected vulnerability in adversarially trained networks from a causal perspective, namely adversarial instrumental variable (IV) regression. By deploying it, we estimate the causal relation of adversarial prediction under an unbiased environment dissociated from unknown confounders. Our approach aims to demystify inherent causal features on adversarial examples by leveraging a zero-sum optimization game between a casual feature estimator (i.e., hypothesis model) and worst-case counterfactuals (i.e., test function) disturbing to find causal features. Through extensive analyses, we demonstrate that the estimated causal features are highly related to the correct prediction for adversarial robustness, and the counterfactuals exhibit extreme features significantly deviating from the correct prediction. In addition, we present how to effectively inoculate CAusal FEatures (CAFE) into defense networks for improving adversarial robustness.

Adversarial examples derived from deliberately crafted perturbations on visual inputs can easily harm decision process of deep neural networks. To prevent potential threats, various adversarial training-based defense methods have grown rapidly and become a de facto standard approach for robustness. Despite recent competitive achievements, we observe that adversarial vulnerability varies across targets and certain vulnerabilities remain prevalent. Intriguingly, such peculiar phenomenon cannot be relieved even with deeper architectures and advanced defense methods. To address this issue, in this paper, we introduce a causal approach called Adversarial Double Machine Learning (ADML), which allows us to quantify the degree of adversarial vulnerability for network predictions and capture the effect of treatments on outcome of interests. ADML can directly estimate causal parameter of adversarial perturbations per se and mitigate negative effects that can potentially damage robustness, bridging a causal perspective into the adversarial vulnerability. Through extensive experiments on various CNN and Transformer architectures, we corroborate that ADML improves adversarial robustness with large margins and relieve the empirical observation.

We propose a new regularization method based on virtual adversarial loss: a new measure of local smoothness of the conditional label distribution given input. Virtual adversarial loss is defined as the robustness of the conditional label distribution around each input data point against local perturbation. Unlike adversarial training, our method defines the adversarial direction without label information and is hence applicable to semi-supervised learning. Because the directions in which we smooth the model are only "virtually" adversarial, we call our method virtual adversarial training (VAT). The computational cost of VAT is relatively low. For neural networks, the approximated gradient of virtual adversarial loss can be computed with no more than two pairs of forward- and back-propagations. In our experiments, we applied VAT to supervised and semi-supervised learning tasks on multiple benchmark datasets. With a simple enhancement of the algorithm based on the entropy minimization principle, our VAT achieves state-of-the-art performance for semi-supervised learning tasks on SVHN and CIFAR-10.

We study Pareto optimality in multi-objective multi-armed bandit by providing a formulation of adversarial multi-objective multi-armed bandit and defining its Pareto regrets that can be applied to both stochastic and adversarial settings. The regrets do not rely on any scalarization functions and reflect Pareto optimality compared to scalarized regrets. We also present new algorithms assuming both with and without prior information of the multi-objective multi-armed bandit setting. The algorithms are shown optimal in adversarial settings and nearly optimal up to a logarithmic factor in stochastic settings simultaneously by our established upper bounds and lower bounds on Pareto regrets. Moreover, the lower bound analyses show that the new regrets are consistent with the existing Pareto regret for stochastic settings and extend an adversarial attack mechanism from bandit to the multi-objective one.

Deep neural networks have been shown to suffer from a surprising weakness: their classification outputs can be changed by small, non-random perturbations of their inputs. This adversarial example phenomenon has been explained as originating from deep networks being "too linear" (Goodfellow et al., 2014). We show here that the linear explanation of adversarial examples presents a number of limitations: the formal argument is not convincing, linear classifiers do not always suffer from the phenomenon, and when they do their adversarial examples are different from the ones affecting deep networks. We propose a new perspective on the phenomenon. We argue that adversarial examples exist when the classification boundary lies close to the submanifold of sampled data, and present a mathematical analysis of this new perspective in the linear case. We define the notion of adversarial strength and show that it can be reduced to the deviation angle between the classifier considered and the nearest centroid classifier. Then, we show that the adversarial strength can be made arbitrarily high independently of the classification performance due to a mechanism that we call boundary tilting. This result leads us to defining a new taxonomy of adversarial examples. Finally, we show that the adversarial strength observed in practice is directly dependent on the level of regularisation used and the strongest adversarial examples, symptomatic of overfitting, can be avoided by using a proper level of regularisation.

We consider learning in an adversarial Markov Decision Process (MDP) where the loss functions can change arbitrarily over K episodes and the state space can be arbitrarily large. We assume that the Q-function of any policy is linear in some known features, that is, a linear function approximation exists. The best existing regret upper bound for this setting (Luo et al., 2021) is of order mathcal O(K^{2/3}) (omitting all other dependencies), given access to a simulator. This paper provides two algorithms that improve the regret to mathcal O(sqrt K) in the same setting. Our first algorithm makes use of a refined analysis of the Follow-the-Regularized-Leader (FTRL) algorithm with the log-barrier regularizer. This analysis allows the loss estimators to be arbitrarily negative and might be of independent interest. Our second algorithm develops a magnitude-reduced loss estimator, further removing the polynomial dependency on the number of actions in the first algorithm and leading to the optimal regret bound (up to logarithmic terms and dependency on the horizon). Moreover, we also extend the first algorithm to simulator-free linear MDPs, which achieves mathcal O(K^{8/9}) regret and greatly improves over the best existing bound mathcal O(K^{14/15}). This algorithm relies on a better alternative to the Matrix Geometric Resampling procedure by Neu & Olkhovskaya (2020), which could again be of independent interest.

Stochastically Extended Adversarial (SEA) model is introduced by Sachs et al. [2022] as an interpolation between stochastic and adversarial online convex optimization. Under the smoothness condition, they demonstrate that the expected regret of optimistic follow-the-regularized-leader (FTRL) depends on the cumulative stochastic variance sigma_{1:T}^2 and the cumulative adversarial variation Sigma_{1:T}^2 for convex functions. They also provide a slightly weaker bound based on the maximal stochastic variance sigma_{max}^2 and the maximal adversarial variation Sigma_{max}^2 for strongly convex functions. Inspired by their work, we investigate the theoretical guarantees of optimistic online mirror descent (OMD) for the SEA model. For convex and smooth functions, we obtain the same O(sigma_{1:T^2}+Sigma_{1:T^2}) regret bound, without the convexity requirement of individual functions. For strongly convex and smooth functions, we establish an O(min{log (sigma_{1:T}^2+Sigma_{1:T}^2), (sigma_{max}^2 + Sigma_{max}^2) log T}) bound, better than their O((sigma_{max}^2 + Sigma_{max}^2) log T) bound. For exp-concave and smooth functions, we achieve a new O(dlog(sigma_{1:T}^2+Sigma_{1:T}^2)) bound. Owing to the OMD framework, we can further extend our result to obtain dynamic regret guarantees, which are more favorable in non-stationary online scenarios. The attained results allow us to recover excess risk bounds of the stochastic setting and regret bounds of the adversarial setting, and derive new guarantees for many intermediate scenarios.

We study a family of adversarial multiclass classification problems and provide equivalent reformulations in terms of: 1) a family of generalized barycenter problems introduced in the paper and 2) a family of multimarginal optimal transport problems where the number of marginals is equal to the number of classes in the original classification problem. These new theoretical results reveal a rich geometric structure of adversarial learning problems in multiclass classification and extend recent results restricted to the binary classification setting. A direct computational implication of our results is that by solving either the barycenter problem and its dual, or the MOT problem and its dual, we can recover the optimal robust classification rule and the optimal adversarial strategy for the original adversarial problem. Examples with synthetic and real data illustrate our results.

Most existing works focus on direct perturbations to the victim's state/action or the underlying transition dynamics to demonstrate the vulnerability of reinforcement learning agents to adversarial attacks. However, such direct manipulations may not be always realizable. In this paper, we consider a multi-agent setting where a well-trained victim agent nu is exploited by an attacker controlling another agent alpha with an adversarial policy. Previous models do not account for the possibility that the attacker may only have partial control over alpha or that the attack may produce easily detectable "abnormal" behaviors. Furthermore, there is a lack of provably efficient defenses against these adversarial policies. To address these limitations, we introduce a generalized attack framework that has the flexibility to model to what extent the adversary is able to control the agent, and allows the attacker to regulate the state distribution shift and produce stealthier adversarial policies. Moreover, we offer a provably efficient defense with polynomial convergence to the most robust victim policy through adversarial training with timescale separation. This stands in sharp contrast to supervised learning, where adversarial training typically provides only empirical defenses. Using the Robosumo competition experiments, we show that our generalized attack formulation results in much stealthier adversarial policies when maintaining the same winning rate as baselines. Additionally, our adversarial training approach yields stable learning dynamics and less exploitable victim policies.

It is becoming increasingly clear that many machine learning classifiers are vulnerable to adversarial examples. In attempting to explain the origin of adversarial examples, previous studies have typically focused on the fact that neural networks operate on high dimensional data, they overfit, or they are too linear. Here we argue that the origin of adversarial examples is primarily due to an inherent uncertainty that neural networks have about their predictions. We show that the functional form of this uncertainty is independent of architecture, dataset, and training protocol; and depends only on the statistics of the logit differences of the network, which do not change significantly during training. This leads to adversarial error having a universal scaling, as a power-law, with respect to the size of the adversarial perturbation. We show that this universality holds for a broad range of datasets (MNIST, CIFAR10, ImageNet, and random data), models (including state-of-the-art deep networks, linear models, adversarially trained networks, and networks trained on randomly shuffled labels), and attacks (FGSM, step l.l., PGD). Motivated by these results, we study the effects of reducing prediction entropy on adversarial robustness. Finally, we study the effect of network architectures on adversarial sensitivity. To do this, we use neural architecture search with reinforcement learning to find adversarially robust architectures on CIFAR10. Our resulting architecture is more robust to white and black box attacks compared to previous attempts.

Value functions are a central component of deep reinforcement learning (RL). These functions, parameterized by neural networks, are trained using a mean squared error regression objective to match bootstrapped target values. However, scaling value-based RL methods that use regression to large networks, such as high-capacity Transformers, has proven challenging. This difficulty is in stark contrast to supervised learning: by leveraging a cross-entropy classification loss, supervised methods have scaled reliably to massive networks. Observing this discrepancy, in this paper, we investigate whether the scalability of deep RL can also be improved simply by using classification in place of regression for training value functions. We demonstrate that value functions trained with categorical cross-entropy significantly improves performance and scalability in a variety of domains. These include: single-task RL on Atari 2600 games with SoftMoEs, multi-task RL on Atari with large-scale ResNets, robotic manipulation with Q-transformers, playing Chess without search, and a language-agent Wordle task with high-capacity Transformers, achieving state-of-the-art results on these domains. Through careful analysis, we show that the benefits of categorical cross-entropy primarily stem from its ability to mitigate issues inherent to value-based RL, such as noisy targets and non-stationarity. Overall, we argue that a simple shift to training value functions with categorical cross-entropy can yield substantial improvements in the scalability of deep RL at little-to-no cost.

The study on improving the robustness of deep neural networks against adversarial examples grows rapidly in recent years. Among them, adversarial training is the most promising one, which flattens the input loss landscape (loss change with respect to input) via training on adversarially perturbed examples. However, how the widely used weight loss landscape (loss change with respect to weight) performs in adversarial training is rarely explored. In this paper, we investigate the weight loss landscape from a new perspective, and identify a clear correlation between the flatness of weight loss landscape and robust generalization gap. Several well-recognized adversarial training improvements, such as early stopping, designing new objective functions, or leveraging unlabeled data, all implicitly flatten the weight loss landscape. Based on these observations, we propose a simple yet effective Adversarial Weight Perturbation (AWP) to explicitly regularize the flatness of weight loss landscape, forming a double-perturbation mechanism in the adversarial training framework that adversarially perturbs both inputs and weights. Extensive experiments demonstrate that AWP indeed brings flatter weight loss landscape and can be easily incorporated into various existing adversarial training methods to further boost their adversarial robustness.

We consider minimizing functions for which it is expensive to compute the (possibly stochastic) gradient. Such functions are prevalent in reinforcement learning, imitation learning and adversarial training. Our target optimization framework uses the (expensive) gradient computation to construct surrogate functions in a target space (e.g. the logits output by a linear model for classification) that can be minimized efficiently. This allows for multiple parameter updates to the model, amortizing the cost of gradient computation. In the full-batch setting, we prove that our surrogate is a global upper-bound on the loss, and can be (locally) minimized using a black-box optimization algorithm. We prove that the resulting majorization-minimization algorithm ensures convergence to a stationary point of the loss. Next, we instantiate our framework in the stochastic setting and propose the SSO algorithm, which can be viewed as projected stochastic gradient descent in the target space. This connection enables us to prove theoretical guarantees for SSO when minimizing convex functions. Our framework allows the use of standard stochastic optimization algorithms to construct surrogates which can be minimized by any deterministic optimization method. To evaluate our framework, we consider a suite of supervised learning and imitation learning problems. Our experiments indicate the benefits of target optimization and the effectiveness of SSO.

Adversarial examples, generated by carefully crafted perturbation, have attracted considerable attention in research fields. Recent works have argued that the existence of the robust and non-robust features is a primary cause of the adversarial examples, and investigated their internal interactions in the feature space. In this paper, we propose a way of explicitly distilling feature representation into the robust and non-robust features, using Information Bottleneck. Specifically, we inject noise variation to each feature unit and evaluate the information flow in the feature representation to dichotomize feature units either robust or non-robust, based on the noise variation magnitude. Through comprehensive experiments, we demonstrate that the distilled features are highly correlated with adversarial prediction, and they have human-perceptible semantic information by themselves. Furthermore, we present an attack mechanism intensifying the gradient of non-robust features that is directly related to the model prediction, and validate its effectiveness of breaking model robustness.

We design learning rate schedules that minimize regret for SGD-based online learning in the presence of a changing data distribution. We fully characterize the optimal learning rate schedule for online linear regression via a novel analysis with stochastic differential equations. For general convex loss functions, we propose new learning rate schedules that are robust to distribution shift, and we give upper and lower bounds for the regret that only differ by constants. For non-convex loss functions, we define a notion of regret based on the gradient norm of the estimated models and propose a learning schedule that minimizes an upper bound on the total expected regret. Intuitively, one expects changing loss landscapes to require more exploration, and we confirm that optimal learning rate schedules typically increase in the presence of distribution shift. Finally, we provide experiments for high-dimensional regression models and neural networks to illustrate these learning rate schedules and their cumulative regret.

We present a method for making neural network predictions robust to shifts from the training data distribution. The proposed method is based on making predictions via a diverse set of cues (called 'middle domains') and ensembling them into one strong prediction. The premise of the idea is that predictions made via different cues respond differently to a distribution shift, hence one should be able to merge them into one robust final prediction. We perform the merging in a straightforward but principled manner based on the uncertainty associated with each prediction. The evaluations are performed using multiple tasks and datasets (Taskonomy, Replica, ImageNet, CIFAR) under a wide range of adversarial and non-adversarial distribution shifts which demonstrate the proposed method is considerably more robust than its standard learning counterpart, conventional deep ensembles, and several other baselines.

Recent work have demonstrated that robustness (to "corruption") can be at odds with generalization. Adversarial training, for instance, aims to reduce the problematic susceptibility of modern neural networks to small data perturbations. Surprisingly, overfitting is a major concern in adversarial training despite being mostly absent in standard training. We provide here theoretical evidence for this peculiar "robust overfitting" phenomenon. Subsequently, we advance a novel distributionally robust loss function bridging robustness and generalization. We demonstrate both theoretically as well as empirically the loss to enjoy a certified level of robustness against two common types of corruption--data evasion and poisoning attacks--while ensuring guaranteed generalization. We show through careful numerical experiments that our resulting holistic robust (HR) training procedure yields SOTA performance. Finally, we indicate that HR training can be interpreted as a direct extension of adversarial training and comes with a negligible additional computational burden. A ready-to-use python library implementing our algorithm is available at https://github.com/RyanLucas3/HR_Neural_Networks.

Most value function learning algorithms in reinforcement learning are based on the mean squared (projected) Bellman error. However, squared errors are known to be sensitive to outliers, both skewing the solution of the objective and resulting in high-magnitude and high-variance gradients. To control these high-magnitude updates, typical strategies in RL involve clipping gradients, clipping rewards, rescaling rewards, or clipping errors. While these strategies appear to be related to robust losses -- like the Huber loss -- they are built on semi-gradient update rules which do not minimize a known loss. In this work, we build on recent insights reformulating squared Bellman errors as a saddlepoint optimization problem and propose a saddlepoint reformulation for a Huber Bellman error and Absolute Bellman error. We start from a formalization of robust losses, then derive sound gradient-based approaches to minimize these losses in both the online off-policy prediction and control settings. We characterize the solutions of the robust losses, providing insight into the problem settings where the robust losses define notably better solutions than the mean squared Bellman error. Finally, we show that the resulting gradient-based algorithms are more stable, for both prediction and control, with less sensitivity to meta-parameters.

We examine the problem of regret minimization when the learner is involved in a continuous game with other optimizing agents: in this case, if all players follow a no-regret algorithm, it is possible to achieve significantly lower regret relative to fully adversarial environments. We study this problem in the context of variationally stable games (a class of continuous games which includes all convex-concave and monotone games), and when the players only have access to noisy estimates of their individual payoff gradients. If the noise is additive, the game-theoretic and purely adversarial settings enjoy similar regret guarantees; however, if the noise is multiplicative, we show that the learners can, in fact, achieve constant regret. We achieve this faster rate via an optimistic gradient scheme with learning rate separation -- that is, the method's extrapolation and update steps are tuned to different schedules, depending on the noise profile. Subsequently, to eliminate the need for delicate hyperparameter tuning, we propose a fully adaptive method that attains nearly the same guarantees as its non-adapted counterpart, while operating without knowledge of either the game or of the noise profile.

Recent works have shown that deep neural networks are vulnerable to adversarial examples that find samples close to the original image but can make the model misclassify. Even with access only to the model's output, an attacker can employ black-box attacks to generate such adversarial examples. In this work, we propose a simple and lightweight defense against black-box attacks by adding random noise to hidden features at intermediate layers of the model at inference time. Our theoretical analysis confirms that this method effectively enhances the model's resilience against both score-based and decision-based black-box attacks. Importantly, our defense does not necessitate adversarial training and has minimal impact on accuracy, rendering it applicable to any pre-trained model. Our analysis also reveals the significance of selectively adding noise to different parts of the model based on the gradient of the adversarial objective function, which can be varied during the attack. We demonstrate the robustness of our defense against multiple black-box attacks through extensive empirical experiments involving diverse models with various architectures.

Counterfactual explanations and adversarial attacks have a related goal: flipping output labels with minimal perturbations regardless of their characteristics. Yet, adversarial attacks cannot be used directly in a counterfactual explanation perspective, as such perturbations are perceived as noise and not as actionable and understandable image modifications. Building on the robust learning literature, this paper proposes an elegant method to turn adversarial attacks into semantically meaningful perturbations, without modifying the classifiers to explain. The proposed approach hypothesizes that Denoising Diffusion Probabilistic Models are excellent regularizers for avoiding high-frequency and out-of-distribution perturbations when generating adversarial attacks. The paper's key idea is to build attacks through a diffusion model to polish them. This allows studying the target model regardless of its robustification level. Extensive experimentation shows the advantages of our counterfactual explanation approach over current State-of-the-Art in multiple testbeds.

It is well-known that the performance of well-trained deep neural networks may degrade significantly when they are applied to data with even slightly shifted distributions. Recent studies have shown that introducing certain perturbation on feature statistics (\eg, mean and standard deviation) during training can enhance the cross-domain generalization ability. Existing methods typically conduct such perturbation by utilizing the feature statistics within a mini-batch, limiting their representation capability. Inspired by the domain generalization objective, we introduce a novel Adversarial Style Augmentation (ASA) method, which explores broader style spaces by generating more effective statistics perturbation via adversarial training. Specifically, we first search for the most sensitive direction and intensity for statistics perturbation by maximizing the task loss. By updating the model against the adversarial statistics perturbation during training, we allow the model to explore the worst-case domain and hence improve its generalization performance. To facilitate the application of ASA, we design a simple yet effective module, namely AdvStyle, which instantiates the ASA method in a plug-and-play manner. We justify the efficacy of AdvStyle on tasks of cross-domain classification and instance retrieval. It achieves higher mean accuracy and lower performance fluctuation. Especially, our method significantly outperforms its competitors on the PACS dataset under the single source generalization setting, \eg, boosting the classification accuracy from 61.2\% to 67.1\% with a ResNet50 backbone. Our code will be available at https://github.com/YBZh/AdvStyle.

Democratization of machine learning requires architectures that automatically adapt to new problems. Neural Differential Equations (NDEs) have emerged as a popular modeling framework by removing the need for ML practitioners to choose the number of layers in a recurrent model. While we can control the computational cost by choosing the number of layers in standard architectures, in NDEs the number of neural network evaluations for a forward pass can depend on the number of steps of the adaptive ODE solver. But, can we force the NDE to learn the version with the least steps while not increasing the training cost? Current strategies to overcome slow prediction require high order automatic differentiation, leading to significantly higher training time. We describe a novel regularization method that uses the internal cost heuristics of adaptive differential equation solvers combined with discrete adjoint sensitivities to guide the training process towards learning NDEs that are easier to solve. This approach opens up the blackbox numerical analysis behind the differential equation solver's algorithm and directly uses its local error estimates and stiffness heuristics as cheap and accurate cost estimates. We incorporate our method without any change in the underlying NDE framework and show that our method extends beyond Ordinary Differential Equations to accommodate Neural Stochastic Differential Equations. We demonstrate how our approach can halve the prediction time and, unlike other methods which can increase the training time by an order of magnitude, we demonstrate similar reduction in training times. Together this showcases how the knowledge embedded within state-of-the-art equation solvers can be used to enhance machine learning.

When users can benefit from certain predictive outcomes, they may be prone to act to achieve those outcome, e.g., by strategically modifying their features. The goal in strategic classification is therefore to train predictive models that are robust to such behavior. However, the conventional framework assumes that changing features does not change actual outcomes, which depicts users as "gaming" the system. Here we remove this assumption, and study learning in a causal strategic setting where true outcomes do change. Focusing on accuracy as our primary objective, we show how strategic behavior and causal effects underlie two complementing forms of distribution shift. We characterize these shifts, and propose a learning algorithm that balances between these two forces and over time, and permits end-to-end training. Experiments on synthetic and semi-synthetic data demonstrate the utility of our approach.

While leveraging additional training data is well established to improve adversarial robustness, it incurs the unavoidable cost of data collection and the heavy computation to train models. To mitigate the costs, we propose Guided Adversarial Training (GAT), a novel adversarial training technique that exploits auxiliary tasks under a limited set of training data. Our approach extends single-task models into multi-task models during the min-max optimization of adversarial training, and drives the loss optimization with a regularization of the gradient curvature across multiple tasks. GAT leverages two types of auxiliary tasks: self-supervised tasks, where the labels are generated automatically, and domain-knowledge tasks, where human experts provide additional labels. Experimentally, GAT increases the robust AUC of CheXpert medical imaging dataset from 50% to 83% and On CIFAR-10, GAT outperforms eight state-of-the-art adversarial training and achieves 56.21% robust accuracy with Resnet-50. Overall, we demonstrate that guided multi-task learning is an actionable and promising avenue to push further the boundaries of model robustness.

Not all learnable parameters (e.g., weights) contribute equally to a neural network's decision function. In fact, entire layers' parameters can sometimes be reset to random values with little to no impact on the model's decisions. We revisit earlier studies that examined how architecture and task complexity influence this phenomenon and ask: is this phenomenon also affected by how we train the model? We conducted experimental evaluations on a diverse set of ImageNet-1k classification models to explore this, keeping the architecture and training data constant but varying the training pipeline. Our findings reveal that the training method strongly influences which layers become critical to the decision function for a given task. For example, improved training regimes and self-supervised training increase the importance of early layers while significantly under-utilizing deeper layers. In contrast, methods such as adversarial training display an opposite trend. Our preliminary results extend previous findings, offering a more nuanced understanding of the inner mechanics of neural networks. Code: https://github.com/paulgavrikov/layer_criticality

Discrete adversarial attacks are symbolic perturbations to a language input that preserve the output label but lead to a prediction error. While such attacks have been extensively explored for the purpose of evaluating model robustness, their utility for improving robustness has been limited to offline augmentation only. Concretely, given a trained model, attacks are used to generate perturbed (adversarial) examples, and the model is re-trained exactly once. In this work, we address this gap and leverage discrete attacks for online augmentation, where adversarial examples are generated at every training step, adapting to the changing nature of the model. We propose (i) a new discrete attack, based on best-first search, and (ii) random sampling attacks that unlike prior work are not based on expensive search-based procedures. Surprisingly, we find that random sampling leads to impressive gains in robustness, outperforming the commonly-used offline augmentation, while leading to a speedup at training time of ~10x. Furthermore, online augmentation with search-based attacks justifies the higher training cost, significantly improving robustness on three datasets. Last, we show that our new attack substantially improves robustness compared to prior methods.

Policy optimization methods are popular reinforcement learning algorithms in practice. Recent works have built theoretical foundation for them by proving T regret bounds even when the losses are adversarial. Such bounds are tight in the worst case but often overly pessimistic. In this work, we show that in tabular Markov decision processes (MDPs), by properly designing the regularizer, the exploration bonus and the learning rates, one can achieve a more favorable polylog(T) regret when the losses are stochastic, without sacrificing the worst-case guarantee in the adversarial regime. To our knowledge, this is also the first time a gap-dependent polylog(T) regret bound is shown for policy optimization. Specifically, we achieve this by leveraging a Tsallis entropy or a Shannon entropy regularizer in the policy update. Then we show that under known transitions, we can further obtain a first-order regret bound in the adversarial regime by leveraging the log-barrier regularizer.

We introduce a novel neural network-based algorithm to compute optimal transport (OT) plans for general cost functionals. In contrast to common Euclidean costs, i.e., ell^1 or ell^2, such functionals provide more flexibility and allow using auxiliary information, such as class labels, to construct the required transport map. Existing methods for general costs are discrete and have limitations in practice, i.e. they do not provide an out-of-sample estimation. We address the challenge of designing a continuous OT approach for general costs that generalizes to new data points in high-dimensional spaces, such as images. Additionally, we provide the theoretical error analysis for our recovered transport plans. As an application, we construct a cost functional to map data distributions while preserving the class-wise structure.

The capabilities and adoption of deep neural networks (DNNs) grow at an exhilarating pace: Vision models accurately classify human actions in videos and identify cancerous tissue in medical scans as precisely than human experts; large language models answer wide-ranging questions, generate code, and write prose, becoming the topic of everyday dinner-table conversations. Even though their uses are exhilarating, the continually increasing model sizes and computational complexities have a dark side. The economic cost and negative environmental externalities of training and serving models is in evident disharmony with financial viability and climate action goals. Instead of pursuing yet another increase in predictive performance, this dissertation is dedicated to the improvement of neural network efficiency. Specifically, a core contribution addresses the efficiency aspects during online inference. Here, the concept of Continual Inference Networks (CINs) is proposed and explored across four publications. CINs extend prior state-of-the-art methods developed for offline processing of spatio-temporal data and reuse their pre-trained weights, improving their online processing efficiency by an order of magnitude. These advances are attained through a bottom-up computational reorganization and judicious architectural modifications. The benefit to online inference is demonstrated by reformulating several widely used network architectures into CINs, including 3D CNNs, ST-GCNs, and Transformer Encoders. An orthogonal contribution tackles the concurrent adaptation and computational acceleration of a large source model into multiple lightweight derived models. Drawing on fusible adapter networks and structured pruning, Structured Pruning Adapters achieve superior predictive accuracy under aggressive pruning using significantly fewer learned weights compared to fine-tuning with pruning.

Catastrophic overfitting (CO) presents a significant challenge in single-step adversarial training (AT), manifesting as highly distorted deep neural networks (DNNs) that are vulnerable to multi-step adversarial attacks. However, the underlying factors that lead to the distortion of decision boundaries remain unclear. In this work, we delve into the specific changes within different DNN layers and discover that during CO, the former layers are more susceptible, experiencing earlier and greater distortion, while the latter layers show relative insensitivity. Our analysis further reveals that this increased sensitivity in former layers stems from the formation of pseudo-robust shortcuts, which alone can impeccably defend against single-step adversarial attacks but bypass genuine-robust learning, resulting in distorted decision boundaries. Eliminating these shortcuts can partially restore robustness in DNNs from the CO state, thereby verifying that dependence on them triggers the occurrence of CO. This understanding motivates us to implement adaptive weight perturbations across different layers to hinder the generation of pseudo-robust shortcuts, consequently mitigating CO. Extensive experiments demonstrate that our proposed method, Layer-Aware Adversarial Weight Perturbation (LAP), can effectively prevent CO and further enhance robustness.

Inverse design, where we seek to design input variables in order to optimize an underlying objective function, is an important problem that arises across fields such as mechanical engineering to aerospace engineering. Inverse design is typically formulated as an optimization problem, with recent works leveraging optimization across learned dynamics models. However, as models are optimized they tend to fall into adversarial modes, preventing effective sampling. We illustrate that by instead optimizing over the learned energy function captured by the diffusion model, we can avoid such adversarial examples and significantly improve design performance. We further illustrate how such a design system is compositional, enabling us to combine multiple different diffusion models representing subcomponents of our desired system to design systems with every specified component. In an N-body interaction task and a challenging 2D multi-airfoil design task, we demonstrate that by composing the learned diffusion model at test time, our method allows us to design initial states and boundary shapes that are more complex than those in the training data. Our method generalizes to more objects for N-body dataset and discovers formation flying to minimize drag in the multi-airfoil design task. Project website and code can be found at https://github.com/AI4Science-WestlakeU/cindm.

Deep neural policies have recently been installed in a diverse range of settings, from biotechnology to automated financial systems. However, the utilization of deep neural networks to approximate the value function leads to concerns on the decision boundary stability, in particular, with regard to the sensitivity of policy decision making to indiscernible, non-robust features due to highly non-convex and complex deep neural manifolds. These concerns constitute an obstruction to understanding the reasoning made by deep neural policies, and their foundational limitations. Hence, it is crucial to develop techniques that aim to understand the sensitivities in the learnt representations of neural network policies. To achieve this we introduce a theoretically founded method that provides a systematic analysis of the unstable directions in the deep neural policy decision boundary across both time and space. Through experiments in the Arcade Learning Environment (ALE), we demonstrate the effectiveness of our technique for identifying correlated directions of instability, and for measuring how sample shifts remold the set of sensitive directions in the neural policy landscape. Most importantly, we demonstrate that state-of-the-art robust training techniques yield learning of disjoint unstable directions, with dramatically larger oscillations over time, when compared to standard training. We believe our results reveal the fundamental properties of the decision process made by reinforcement learning policies, and can help in constructing reliable and robust deep neural policies.

This paper studies online nonstochastic control problems with adversarial and static constraints. We propose online nonstochastic control algorithms that achieve both sublinear regret and sublinear adversarial constraint violation while keeping static constraint violation minimal against the optimal constrained linear control policy in hindsight. To establish the results, we introduce an online convex optimization with memory framework under adversarial and static constraints, which serves as a subroutine for the constrained online nonstochastic control algorithms. This subroutine also achieves the state-of-the-art regret and constraint violation bounds for constrained online convex optimization problems, which is of independent interest. Our experiments demonstrate the proposed control algorithms are adaptive to adversarial constraints and achieve smaller cumulative costs and violations. Moreover, our algorithms are less conservative and achieve significantly smaller cumulative costs than the state-of-the-art algorithm.

Aligning generative models with human preference via RLHF typically suffers from overoptimization, where an imperfectly learned reward model can misguide the generative model to output undesired responses. We investigate this problem in a principled manner by identifying the source of the misalignment as a form of distributional shift and uncertainty in learning human preferences. To mitigate overoptimization, we first propose a theoretical algorithm that chooses the best policy for an adversarially chosen reward model; one that simultaneously minimizes the maximum likelihood estimation of the loss and a reward penalty term. Here, the reward penalty term is introduced to prevent the policy from choosing actions with spurious high proxy rewards, resulting in provable sample efficiency of the algorithm under a partial coverage style condition. Moving from theory to practice, the proposed algorithm further enjoys an equivalent but surprisingly easy-to-implement reformulation. Using the equivalence between reward models and the corresponding optimal policy, the algorithm features a simple objective that combines: (i) a preference optimization loss that directly aligns the policy with human preference, and (ii) a supervised learning loss that explicitly imitates the policy with a (suitable) baseline distribution. In the context of aligning large language models (LLM), this objective fuses the direct preference optimization (DPO) loss with the supervised fune-tuning (SFT) loss to help mitigate the overoptimization towards undesired responses, for which we name the algorithm Regularized Preference Optimization (RPO). Experiments of aligning LLMs demonstrate the improved performance of RPO compared with DPO baselines. Our work sheds light on the interplay between preference optimization and SFT in tuning LLMs with both theoretical guarantees and empirical evidence.

We apply supervised deep neural networks (DNNs) for pricing and calibration of both vanilla and exotic options under both diffusion and pure jump processes with and without stochastic volatility. We train our neural network models under different number of layers, neurons per layer, and various different activation functions in order to find which combinations work better empirically. For training, we consider various different loss functions and optimization routines. We demonstrate that deep neural networks exponentially expedite option pricing compared to commonly used option pricing methods which consequently make calibration and parameter estimation super fast.

Robust optimization provides a mathematical framework for modeling and solving decision-making problems under worst-case uncertainty. This work addresses two-stage robust optimization (2RO) problems (also called adjustable robust optimization), wherein first-stage and second-stage decisions are made before and after uncertainty is realized, respectively. This results in a nested min-max-min optimization problem which is extremely challenging computationally, especially when the decisions are discrete. We propose Neur2RO, an efficient machine learning-driven instantiation of column-and-constraint generation (CCG), a classical iterative algorithm for 2RO. Specifically, we learn to estimate the value function of the second-stage problem via a novel neural network architecture that is easy to optimize over by design. Embedding our neural network into CCG yields high-quality solutions quickly as evidenced by experiments on two 2RO benchmarks, knapsack and capital budgeting. For knapsack, Neur2RO finds solutions that are within roughly 2% of the best-known values in a few seconds compared to the three hours of the state-of-the-art exact branch-and-price algorithm; for larger and more complex instances, Neur2RO finds even better solutions. For capital budgeting, Neur2RO outperforms three variants of the k-adaptability algorithm, particularly on the largest instances, with a 10 to 100-fold reduction in solution time. Our code and data are available at https://github.com/khalil-research/Neur2RO.

While prior research has proposed a plethora of methods that build neural classifiers robust against adversarial robustness, practitioners are still reluctant to adopt them due to their unacceptably severe clean accuracy penalties. This paper significantly alleviates this accuracy-robustness trade-off by mixing the output probabilities of a standard classifier and a robust classifier, where the standard network is optimized for clean accuracy and is not robust in general. We show that the robust base classifier's confidence difference for correct and incorrect examples is the key to this improvement. In addition to providing intuitions and empirical evidence, we theoretically certify the robustness of the mixed classifier under realistic assumptions. Furthermore, we adapt an adversarial input detector into a mixing network that adaptively adjusts the mixture of the two base models, further reducing the accuracy penalty of achieving robustness. The proposed flexible method, termed "adaptive smoothing", can work in conjunction with existing or even future methods that improve clean accuracy, robustness, or adversary detection. Our empirical evaluation considers strong attack methods, including AutoAttack and adaptive attack. On the CIFAR-100 dataset, our method achieves an 85.21% clean accuracy while maintaining a 38.72% ell_infty-AutoAttacked (epsilon = 8/255) accuracy, becoming the second most robust method on the RobustBench CIFAR-100 benchmark as of submission, while improving the clean accuracy by ten percentage points compared with all listed models. The code that implements our method is available at https://github.com/Bai-YT/AdaptiveSmoothing.

We propose an algorithm for inexpensive gradient-based hyperparameter optimization that combines the implicit function theorem (IFT) with efficient inverse Hessian approximations. We present results about the relationship between the IFT and differentiating through optimization, motivating our algorithm. We use the proposed approach to train modern network architectures with millions of weights and millions of hyper-parameters. For example, we learn a data-augmentation network - where every weight is a hyperparameter tuned for validation performance - outputting augmented training examples. Jointly tuning weights and hyperparameters with our approach is only a few times more costly in memory and compute than standard training.

Probabilistic dynamics model ensemble is widely used in existing model-based reinforcement learning methods as it outperforms a single dynamics model in both asymptotic performance and sample efficiency. In this paper, we provide both practical and theoretical insights on the empirical success of the probabilistic dynamics model ensemble through the lens of Lipschitz continuity. We find that, for a value function, the stronger the Lipschitz condition is, the smaller the gap between the true dynamics- and learned dynamics-induced Bellman operators is, thus enabling the converged value function to be closer to the optimal value function. Hence, we hypothesize that the key functionality of the probabilistic dynamics model ensemble is to regularize the Lipschitz condition of the value function using generated samples. To test this hypothesis, we devise two practical robust training mechanisms through computing the adversarial noise and regularizing the value network's spectral norm to directly regularize the Lipschitz condition of the value functions. Empirical results show that combined with our mechanisms, model-based RL algorithms with a single dynamics model outperform those with an ensemble of probabilistic dynamics models. These findings not only support the theoretical insight, but also provide a practical solution for developing computationally efficient model-based RL algorithms.

We introduce the use of generative adversarial learning to compute equilibria in general game-theoretic settings, specifically the generalized Nash equilibrium (GNE) in pseudo-games, and its specific instantiation as the competitive equilibrium (CE) in Arrow-Debreu competitive economies. Pseudo-games are a generalization of games in which players' actions affect not only the payoffs of other players but also their feasible action spaces. Although the computation of GNE and CE is intractable in the worst-case, i.e., PPAD-hard, in practice, many applications only require solutions with high accuracy in expectation over a distribution of problem instances. We introduce Generative Adversarial Equilibrium Solvers (GAES): a family of generative adversarial neural networks that can learn GNE and CE from only a sample of problem instances. We provide computational and sample complexity bounds, and apply the framework to finding Nash equilibria in normal-form games, CE in Arrow-Debreu competitive economies, and GNE in an environmental economic model of the Kyoto mechanism.

Implicit layer deep learning techniques, like Neural Differential Equations, have become an important modeling framework due to their ability to adapt to new problems automatically. Training a neural differential equation is effectively a search over a space of plausible dynamical systems. However, controlling the computational cost for these models is difficult since it relies on the number of steps the adaptive solver takes. Most prior works have used higher-order methods to reduce prediction timings while greatly increasing training time or reducing both training and prediction timings by relying on specific training algorithms, which are harder to use as a drop-in replacement due to strict requirements on automatic differentiation. In this manuscript, we use internal cost heuristics of adaptive differential equation solvers at stochastic time points to guide the training toward learning a dynamical system that is easier to integrate. We "close the black-box" and allow the use of our method with any adjoint technique for gradient calculations of the differential equation solution. We perform experimental studies to compare our method to global regularization to show that we attain similar performance numbers without compromising the flexibility of implementation on ordinary differential equations (ODEs) and stochastic differential equations (SDEs). We develop two sampling strategies to trade off between performance and training time. Our method reduces the number of function evaluations to 0.556-0.733x and accelerates predictions by 1.3-2x.

We study the design of loss functions for click-through rates (CTR) to optimize (social) welfare in advertising auctions. Existing works either only focus on CTR predictions without consideration of business objectives (e.g., welfare) in auctions or assume that the distribution over the participants' expected cost-per-impression (eCPM) is known a priori, then use various additional assumptions on the parametric form of the distribution to derive loss functions for predicting CTRs. In this work, we bring back the welfare objectives of ad auctions into CTR predictions and propose a novel weighted rankloss to train the CTR model. Compared to existing literature, our approach provides a provable guarantee on welfare but without assumptions on the eCPMs' distribution while also avoiding the intractability of naively applying existing learning-to-rank methods. Further, we propose a theoretically justifiable technique for calibrating the losses using labels generated from a teacher network, only assuming that the teacher network has bounded ell_2 generalization error. Finally, we demonstrate the advantages of the proposed loss on synthetic and real-world data.

Users like sharing personal photos with others through social media. At the same time, they might want to make automatic identification in such photos difficult or even impossible. Classic obfuscation methods such as blurring are not only unpleasant but also not as effective as one would expect. Recent studies on adversarial image perturbations (AIP) suggest that it is possible to confuse recognition systems effectively without unpleasant artifacts. However, in the presence of counter measures against AIPs, it is unclear how effective AIP would be in particular when the choice of counter measure is unknown. Game theory provides tools for studying the interaction between agents with uncertainties in the strategies. We introduce a general game theoretical framework for the user-recogniser dynamics, and present a case study that involves current state of the art AIP and person recognition techniques. We derive the optimal strategy for the user that assures an upper bound on the recognition rate independent of the recogniser's counter measure. Code is available at https://goo.gl/hgvbNK.

Primal-dual safe RL methods commonly perform iterations between the primal update of the policy and the dual update of the Lagrange Multiplier. Such a training paradigm is highly susceptible to the error in cumulative cost estimation since this estimation serves as the key bond connecting the primal and dual update processes. We show that this problem causes significant underestimation of cost when using off-policy methods, leading to the failure to satisfy the safety constraint. To address this issue, we propose conservative policy optimization, which learns a policy in a constraint-satisfying area by considering the uncertainty in cost estimation. This improves constraint satisfaction but also potentially hinders reward maximization. We then introduce local policy convexification to help eliminate such suboptimality by gradually reducing the estimation uncertainty. We provide theoretical interpretations of the joint coupling effect of these two ingredients and further verify them by extensive experiments. Results on benchmark tasks show that our method not only achieves an asymptotic performance comparable to state-of-the-art on-policy methods while using much fewer samples, but also significantly reduces constraint violation during training. Our code is available at https://github.com/ZifanWu/CAL.

Adversarial attacks expose important vulnerabilities of deep learning models, yet little attention has been paid to settings where data arrives as a stream. In this paper, we formalize the online adversarial attack problem, emphasizing two key elements found in real-world use-cases: attackers must operate under partial knowledge of the target model, and the decisions made by the attacker are irrevocable since they operate on a transient data stream. We first rigorously analyze a deterministic variant of the online threat model by drawing parallels to the well-studied k-secretary problem in theoretical computer science and propose Virtual+, a simple yet practical online algorithm. Our main theoretical result shows Virtual+ yields provably the best competitive ratio over all single-threshold algorithms for k<5 -- extending the previous analysis of the k-secretary problem. We also introduce the stochastic k-secretary -- effectively reducing online blackbox transfer attacks to a k-secretary problem under noise -- and prove theoretical bounds on the performance of Virtual+ adapted to this setting. Finally, we complement our theoretical results by conducting experiments on MNIST, CIFAR-10, and Imagenet classifiers, revealing the necessity of online algorithms in achieving near-optimal performance and also the rich interplay between attack strategies and online attack selection, enabling simple strategies like FGSM to outperform stronger adversaries.

Recent work has shown that the training of a one-hidden-layer, scalar-output fully-connected ReLU neural network can be reformulated as a finite-dimensional convex program. Unfortunately, the scale of such a convex program grows exponentially in data size. In this work, we prove that a stochastic procedure with a linear complexity well approximates the exact formulation. Moreover, we derive a convex optimization approach to efficiently solve the "adversarial training" problem, which trains neural networks that are robust to adversarial input perturbations. Our method can be applied to binary classification and regression, and provides an alternative to the current adversarial training methods, such as Fast Gradient Sign Method (FGSM) and Projected Gradient Descent (PGD). We demonstrate in experiments that the proposed method achieves a noticeably better adversarial robustness and performance than the existing methods.

Reliable deployment of machine learning models such as neural networks continues to be challenging due to several limitations. Some of the main shortcomings are the lack of interpretability and the lack of robustness against adversarial examples or out-of-distribution inputs. In this exploratory review, we explore the possibilities and limits of adversarial attacks for explainable machine learning models. First, we extend the notion of adversarial examples to fit in explainable machine learning scenarios, in which the inputs, the output classifications and the explanations of the model's decisions are assessed by humans. Next, we propose a comprehensive framework to study whether (and how) adversarial examples can be generated for explainable models under human assessment, introducing and illustrating novel attack paradigms. In particular, our framework considers a wide range of relevant yet often ignored factors such as the type of problem, the user expertise or the objective of the explanations, in order to identify the attack strategies that should be adopted in each scenario to successfully deceive the model (and the human). The intention of these contributions is to serve as a basis for a more rigorous and realistic study of adversarial examples in the field of explainable machine learning.

Machine learning approaches relying on such criteria as adversarial robustness or multi-agent settings have raised the need for solving game-theoretic equilibrium problems. Of particular relevance to these applications are methods targeting finite-sum structure, which generically arises in empirical variants of learning problems in these contexts. Further, methods with computable approximation errors are highly desirable, as they provide verifiable exit criteria. Motivated by these applications, we study finite-sum monotone inclusion problems, which model broad classes of equilibrium problems. Our main contributions are variants of the classical Halpern iteration that employ variance reduction to obtain improved complexity guarantees in which n component operators in the finite sum are ``on average'' either cocoercive or Lipschitz continuous and monotone, with parameter L. The resulting oracle complexity of our methods, which provide guarantees for the last iterate and for a (computable) operator norm residual, is mathcal{O}( n + nLvarepsilon^{-1}), which improves upon existing methods by a factor up to n. This constitutes the first variance reduction-type result for general finite-sum monotone inclusions and for more specific problems such as convex-concave optimization when operator norm residual is the optimality measure. We further argue that, up to poly-logarithmic factors, this complexity is unimprovable in the monotone Lipschitz setting; i.e., the provided result is near-optimal.

Consider learning a policy from example expert behavior, without interaction with the expert or access to reinforcement signal. One approach is to recover the expert's cost function with inverse reinforcement learning, then extract a policy from that cost function with reinforcement learning. This approach is indirect and can be slow. We propose a new general framework for directly extracting a policy from data, as if it were obtained by reinforcement learning following inverse reinforcement learning. We show that a certain instantiation of our framework draws an analogy between imitation learning and generative adversarial networks, from which we derive a model-free imitation learning algorithm that obtains significant performance gains over existing model-free methods in imitating complex behaviors in large, high-dimensional environments.

As machine learning models grow in complexity and increasingly rely on publicly sourced data, such as the human-annotated labels used in training large language models, they become more vulnerable to label poisoning attacks. These attacks, in which adversaries subtly alter the labels within a training dataset, can severely degrade model performance, posing significant risks in critical applications. In this paper, we propose FLORAL, a novel adversarial training defense strategy based on support vector machines (SVMs) to counter these threats. Utilizing a bilevel optimization framework, we cast the training process as a non-zero-sum Stackelberg game between an attacker, who strategically poisons critical training labels, and the model, which seeks to recover from such attacks. Our approach accommodates various model architectures and employs a projected gradient descent algorithm with kernel SVMs for adversarial training. We provide a theoretical analysis of our algorithm's convergence properties and empirically evaluate FLORAL's effectiveness across diverse classification tasks. Compared to robust baselines and foundation models such as RoBERTa, FLORAL consistently achieves higher robust accuracy under increasing attacker budgets. These results underscore the potential of FLORAL to enhance the resilience of machine learning models against label poisoning threats, thereby ensuring robust classification in adversarial settings.

Recent studies have revealed the vulnerability of Deep Neural Networks (DNNs) to adversarial examples, which can easily fool DNNs into making incorrect predictions. To mitigate this deficiency, we propose a novel adversarial defense method called "Immunity" (Innovative MoE with MUtual information \& positioN stabilITY) based on a modified Mixture-of-Experts (MoE) architecture in this work. The key enhancements to the standard MoE are two-fold: 1) integrating of Random Switch Gates (RSGs) to obtain diverse network structures via random permutation of RSG parameters at evaluation time, despite of RSGs being determined after one-time training; 2) devising innovative Mutual Information (MI)-based and Position Stability-based loss functions by capitalizing on Grad-CAM's explanatory power to increase the diversity and the causality of expert networks. Notably, our MI-based loss operates directly on the heatmaps, thereby inducing subtler negative impacts on the classification performance when compared to other losses of the same type, theoretically. Extensive evaluation validates the efficacy of the proposed approach in improving adversarial robustness against a wide range of attacks.

Robustness against adversarial attacks and distribution shifts is a long-standing goal of Reinforcement Learning (RL). To this end, Robust Adversarial Reinforcement Learning (RARL) trains a protagonist against destabilizing forces exercised by an adversary in a competitive zero-sum Markov game, whose optimal solution, i.e., rational strategy, corresponds to a Nash equilibrium. However, finding Nash equilibria requires facing complex saddle point optimization problems, which can be prohibitive to solve, especially for high-dimensional control. In this paper, we propose a novel approach for adversarial RL based on entropy regularization to ease the complexity of the saddle point optimization problem. We show that the solution of this entropy-regularized problem corresponds to a Quantal Response Equilibrium (QRE), a generalization of Nash equilibria that accounts for bounded rationality, i.e., agents sometimes play random actions instead of optimal ones. Crucially, the connection between the entropy-regularized objective and QRE enables free modulation of the rationality of the agents by simply tuning the temperature coefficient. We leverage this insight to propose our novel algorithm, Quantal Adversarial RL (QARL), which gradually increases the rationality of the adversary in a curriculum fashion until it is fully rational, easing the complexity of the optimization problem while retaining robustness. We provide extensive evidence of QARL outperforming RARL and recent baselines across several MuJoCo locomotion and navigation problems in overall performance and robustness.

Discovering the existence of universal adversarial perturbations had large theoretical and practical impacts on the field of adversarial learning. In the text domain, most universal studies focused on adversarial prefixes which are added to all texts. However, unlike the vision domain, adding the same perturbation to different inputs results in noticeably unnatural inputs. Therefore, we introduce a new universal adversarial setup - a universal adversarial policy, which has many advantages of other universal attacks but also results in valid texts - thus making it relevant in practice. We achieve this by learning a single search policy over a predefined set of semantics preserving text alterations, on many texts. This formulation is universal in that the policy is successful in finding adversarial examples on new texts efficiently. Our approach uses text perturbations which were extensively shown to produce natural attacks in the non-universal setup (specific synonym replacements). We suggest a strong baseline approach for this formulation which uses reinforcement learning. It's ability to generalise (from as few as 500 training texts) shows that universal adversarial patterns exist in the text domain as well.

Designing control policies whose performance level is guaranteed to remain above a given threshold in a span of environments is a critical feature for the adoption of reinforcement learning (RL) in real-world applications. The search for such robust policies is a notoriously difficult problem, related to the so-called dynamic model of transition function uncertainty, where the environment dynamics are allowed to change at each time step. But in practical cases, one is rather interested in robustness to a span of static transition models throughout interaction episodes. The static model is known to be harder to solve than the dynamic one, and seminal algorithms, such as robust value iteration, as well as most recent works on deep robust RL, build upon the dynamic model. In this work, we propose to revisit the static model. We suggest an analysis of why solving the static model under some mild hypotheses is a reasonable endeavor, based on an equivalence with the dynamic model, and formalize the general intuition that robust MDPs can be solved by tackling a series of static problems. We introduce a generic meta-algorithm called IWOCS, which incrementally identifies worst-case transition models so as to guide the search for a robust policy. Discussion on IWOCS sheds light on new ways to decouple policy optimization and adversarial transition functions and opens new perspectives for analysis. We derive a deep RL version of IWOCS and demonstrate it is competitive with state-of-the-art algorithms on classical benchmarks.

Machine learning models are vulnerable to adversarial perturbations, and a thought-provoking paper by Bubeck and Sellke has analyzed this phenomenon through the lens of over-parameterization: interpolating smoothly the data requires significantly more parameters than simply memorizing it. However, this "universal" law provides only a necessary condition for robustness, and it is unable to discriminate between models. In this paper, we address these gaps by focusing on empirical risk minimization in two prototypical settings, namely, random features and the neural tangent kernel (NTK). We prove that, for random features, the model is not robust for any degree of over-parameterization, even when the necessary condition coming from the universal law of robustness is satisfied. In contrast, for even activations, the NTK model meets the universal lower bound, and it is robust as soon as the necessary condition on over-parameterization is fulfilled. This also addresses a conjecture in prior work by Bubeck, Li and Nagaraj. Our analysis decouples the effect of the kernel of the model from an "interaction matrix", which describes the interaction with the test data and captures the effect of the activation. Our theoretical results are corroborated by numerical evidence on both synthetic and standard datasets (MNIST, CIFAR-10).

We propose a simple data augmentation technique that can be applied to standard model-free reinforcement learning algorithms, enabling robust learning directly from pixels without the need for auxiliary losses or pre-training. The approach leverages input perturbations commonly used in computer vision tasks to regularize the value function. Existing model-free approaches, such as Soft Actor-Critic (SAC), are not able to train deep networks effectively from image pixels. However, the addition of our augmentation method dramatically improves SAC's performance, enabling it to reach state-of-the-art performance on the DeepMind control suite, surpassing model-based (Dreamer, PlaNet, and SLAC) methods and recently proposed contrastive learning (CURL). Our approach can be combined with any model-free reinforcement learning algorithm, requiring only minor modifications. An implementation can be found at https://sites.google.com/view/data-regularized-q.

Domain adaptation aims to mitigate distribution shifts among different domains. However, traditional formulations are mostly limited to categorical domains, greatly simplifying nuanced domain relationships in the real world. In this work, we tackle a generalization with taxonomy-structured domains, which formalizes domains with nested, hierarchical similarity structures such as animal species and product catalogs. We build on the classic adversarial framework and introduce a novel taxonomist, which competes with the adversarial discriminator to preserve the taxonomy information. The equilibrium recovers the classic adversarial domain adaptation's solution if given a non-informative domain taxonomy (e.g., a flat taxonomy where all leaf nodes connect to the root node) while yielding non-trivial results with other taxonomies. Empirically, our method achieves state-of-the-art performance on both synthetic and real-world datasets with successful adaptation. Code is available at https://github.com/Wang-ML-Lab/TSDA.

The phenomenon of adversarial examples illustrates one of the most basic vulnerabilities of deep neural networks. Among the variety of techniques introduced to surmount this inherent weakness, adversarial training has emerged as the most effective strategy for learning robust models. Typically, this is achieved by balancing robust and natural objectives. In this work, we aim to further optimize the trade-off between robust and standard accuracy by enforcing a domain-invariant feature representation. We present a new adversarial training method, Domain Invariant Adversarial Learning (DIAL), which learns a feature representation that is both robust and domain invariant. DIAL uses a variant of Domain Adversarial Neural Network (DANN) on the natural domain and its corresponding adversarial domain. In the case where the source domain consists of natural examples and the target domain is the adversarially perturbed examples, our method learns a feature representation constrained not to discriminate between the natural and adversarial examples, and can therefore achieve a more robust representation. DIAL is a generic and modular technique that can be easily incorporated into any adversarial training method. Our experiments indicate that incorporating DIAL in the adversarial training process improves both robustness and standard accuracy.

The bandits with knapsack (BwK) framework models online decision-making problems in which an agent makes a sequence of decisions subject to resource consumption constraints. The traditional model assumes that each action consumes a non-negative amount of resources and the process ends when the initial budgets are fully depleted. We study a natural generalization of the BwK framework which allows non-monotonic resource utilization, i.e., resources can be replenished by a positive amount. We propose a best-of-both-worlds primal-dual template that can handle any online learning problem with replenishment for which a suitable primal regret minimizer exists. In particular, we provide the first positive results for the case of adversarial inputs by showing that our framework guarantees a constant competitive ratio alpha when B=Omega(T) or when the possible per-round replenishment is a positive constant. Moreover, under a stochastic input model, our algorithm yields an instance-independent O(T^{1/2}) regret bound which complements existing instance-dependent bounds for the same setting. Finally, we provide applications of our framework to some economic problems of practical relevance.

Standard methods for generating adversarial examples for neural networks do not consistently fool neural network classifiers in the physical world due to a combination of viewpoint shifts, camera noise, and other natural transformations, limiting their relevance to real-world systems. We demonstrate the existence of robust 3D adversarial objects, and we present the first algorithm for synthesizing examples that are adversarial over a chosen distribution of transformations. We synthesize two-dimensional adversarial images that are robust to noise, distortion, and affine transformation. We apply our algorithm to complex three-dimensional objects, using 3D-printing to manufacture the first physical adversarial objects. Our results demonstrate the existence of 3D adversarial objects in the physical world.

Robust loss functions are essential for training accurate deep neural networks (DNNs) in the presence of noisy (incorrect) labels. It has been shown that the commonly used Cross Entropy (CE) loss is not robust to noisy labels. Whilst new loss functions have been designed, they are only partially robust. In this paper, we theoretically show by applying a simple normalization that: any loss can be made robust to noisy labels. However, in practice, simply being robust is not sufficient for a loss function to train accurate DNNs. By investigating several robust loss functions, we find that they suffer from a problem of underfitting. To address this, we propose a framework to build robust loss functions called Active Passive Loss (APL). APL combines two robust loss functions that mutually boost each other. Experiments on benchmark datasets demonstrate that the family of new loss functions created by our APL framework can consistently outperform state-of-the-art methods by large margins, especially under large noise rates such as 60% or 80% incorrect labels.

Adversarial examples pose a significant challenge to the robustness, reliability and alignment of deep neural networks. We propose a novel, easy-to-use approach to achieving high-quality representations that lead to adversarial robustness through the use of multi-resolution input representations and dynamic self-ensembling of intermediate layer predictions. We demonstrate that intermediate layer predictions exhibit inherent robustness to adversarial attacks crafted to fool the full classifier, and propose a robust aggregation mechanism based on Vickrey auction that we call CrossMax to dynamically ensemble them. By combining multi-resolution inputs and robust ensembling, we achieve significant adversarial robustness on CIFAR-10 and CIFAR-100 datasets without any adversarial training or extra data, reaching an adversarial accuracy of approx72% (CIFAR-10) and approx48% (CIFAR-100) on the RobustBench AutoAttack suite (L_infty=8/255) with a finetuned ImageNet-pretrained ResNet152. This represents a result comparable with the top three models on CIFAR-10 and a +5 % gain compared to the best current dedicated approach on CIFAR-100. Adding simple adversarial training on top, we get approx78% on CIFAR-10 and approx51% on CIFAR-100, improving SOTA by 5 % and 9 % respectively and seeing greater gains on the harder dataset. We validate our approach through extensive experiments and provide insights into the interplay between adversarial robustness, and the hierarchical nature of deep representations. We show that simple gradient-based attacks against our model lead to human-interpretable images of the target classes as well as interpretable image changes. As a byproduct, using our multi-resolution prior, we turn pre-trained classifiers and CLIP models into controllable image generators and develop successful transferable attacks on large vision language models.

Overfitting widely exists in adversarial robust training of deep networks. An effective remedy is adversarial weight perturbation, which injects the worst-case weight perturbation during network training by maximizing the classification loss on adversarial examples. Adversarial weight perturbation helps reduce the robust generalization gap; however, it also undermines the robustness improvement. A criterion that regulates the weight perturbation is therefore crucial for adversarial training. In this paper, we propose such a criterion, namely Loss Stationary Condition (LSC) for constrained perturbation. With LSC, we find that it is essential to conduct weight perturbation on adversarial data with small classification loss to eliminate robust overfitting. Weight perturbation on adversarial data with large classification loss is not necessary and may even lead to poor robustness. Based on these observations, we propose a robust perturbation strategy to constrain the extent of weight perturbation. The perturbation strategy prevents deep networks from overfitting while avoiding the side effect of excessive weight perturbation, significantly improving the robustness of adversarial training. Extensive experiments demonstrate the superiority of the proposed method over the state-of-the-art adversarial training methods.

In standard adversarial training, models are optimized to fit one-hot labels within allowable adversarial perturbation budgets. However, the ignorance of underlying distribution shifts brought by perturbations causes the problem of robust overfitting. To address this issue and enhance adversarial robustness, we analyze the characteristics of robust models and identify that robust models tend to produce smoother and well-calibrated outputs. Based on the observation, we propose a simple yet effective method, Annealing Self-Distillation Rectification (ADR), which generates soft labels as a better guidance mechanism that accurately reflects the distribution shift under attack during adversarial training. By utilizing ADR, we can obtain rectified distributions that significantly improve model robustness without the need for pre-trained models or extensive extra computation. Moreover, our method facilitates seamless plug-and-play integration with other adversarial training techniques by replacing the hard labels in their objectives. We demonstrate the efficacy of ADR through extensive experiments and strong performances across datasets.

Assigning importance weights to adversarial data has achieved great success in training adversarially robust networks under limited model capacity. However, existing instance-reweighted adversarial training (AT) methods heavily depend on heuristics and/or geometric interpretations to determine those importance weights, making these algorithms lack rigorous theoretical justification/guarantee. Moreover, recent research has shown that adversarial training suffers from a severe non-uniform robust performance across the training distribution, e.g., data points belonging to some classes can be much more vulnerable to adversarial attacks than others. To address both issues, in this paper, we propose a novel doubly-robust instance reweighted AT framework, which allows to obtain the importance weights via exploring distributionally robust optimization (DRO) techniques, and at the same time boosts the robustness on the most vulnerable examples. In particular, our importance weights are obtained by optimizing the KL-divergence regularized loss function, which allows us to devise new algorithms with a theoretical convergence guarantee. Experiments on standard classification datasets demonstrate that our proposed approach outperforms related state-of-the-art baseline methods in terms of average robust performance, and at the same time improves the robustness against attacks on the weakest data points. Codes will be available soon.

In Causal Bayesian Optimization (CBO), an agent intervenes on an unknown structural causal model to maximize a downstream reward variable. In this paper, we consider the generalization where other agents or external events also intervene on the system, which is key for enabling adaptiveness to non-stationarities such as weather changes, market forces, or adversaries. We formalize this generalization of CBO as Adversarial Causal Bayesian Optimization (ACBO) and introduce the first algorithm for ACBO with bounded regret: Causal Bayesian Optimization with Multiplicative Weights (CBO-MW). Our approach combines a classical online learning strategy with causal modeling of the rewards. To achieve this, it computes optimistic counterfactual reward estimates by propagating uncertainty through the causal graph. We derive regret bounds for CBO-MW that naturally depend on graph-related quantities. We further propose a scalable implementation for the case of combinatorial interventions and submodular rewards. Empirically, CBO-MW outperforms non-causal and non-adversarial Bayesian optimization methods on synthetic environments and environments based on real-word data. Our experiments include a realistic demonstration of how CBO-MW can be used to learn users' demand patterns in a shared mobility system and reposition vehicles in strategic areas.

This paper investigates the use of prior computation to estimate the value function to improve sample efficiency in on-policy policy gradient methods in reinforcement learning. Our approach is to estimate the value function from prior computations, such as from the Q-network learned in DQN or the value function trained for different but related environments. In particular, we learn a new value function for the target task while combining it with a value estimate from the prior computation. Finally, the resulting value function is used as a baseline in the policy gradient method. This use of a baseline has the theoretical property of reducing variance in gradient computation and thus improving sample efficiency. The experiments show the successful use of prior value estimates in various settings and improved sample efficiency in several tasks.

Effective regularization techniques are highly desired in deep learning for alleviating overfitting and improving generalization. This work proposes a new regularization scheme, based on the understanding that the flat local minima of the empirical risk cause the model to generalize better. This scheme is referred to as adversarial model perturbation (AMP), where instead of directly minimizing the empirical risk, an alternative "AMP loss" is minimized via SGD. Specifically, the AMP loss is obtained from the empirical risk by applying the "worst" norm-bounded perturbation on each point in the parameter space. Comparing with most existing regularization schemes, AMP has strong theoretical justifications, in that minimizing the AMP loss can be shown theoretically to favour flat local minima of the empirical risk. Extensive experiments on various modern deep architectures establish AMP as a new state of the art among regularization schemes. Our code is available at https://github.com/hiyouga/AMP-Regularizer.

Adversarial robustness has been conventionally believed as a challenging property to encode for neural networks, requiring plenty of training data. In the recent paradigm of adopting off-the-shelf models, however, access to their training data is often infeasible or not practical, while most of such models are not originally trained concerning adversarial robustness. In this paper, we develop a scalable and model-agnostic solution to achieve adversarial robustness without using any data. Our intuition is to view recent text-to-image diffusion models as "adaptable" denoisers that can be optimized to specify target tasks. Based on this, we propose: (a) to initiate a denoise-and-classify pipeline that offers provable guarantees against adversarial attacks, and (b) to leverage a few synthetic reference images generated from the text-to-image model that enables novel adaptation schemes. Our experiments show that our data-free scheme applied to the pre-trained CLIP could improve the (provable) adversarial robustness of its diverse zero-shot classification derivatives (while maintaining their accuracy), significantly surpassing prior approaches that utilize the full training data. Not only for CLIP, we also demonstrate that our framework is easily applicable for robustifying other visual classifiers efficiently.

Training deep neural networks on images represented as grids of pixels has brought to light an interesting phenomenon known as adversarial examples. Inspired by how humans reconstruct abstract concepts, we attempt to codify the input bitmap image into a set of compact, interpretable elements to avoid being fooled by the adversarial structures. We take the first step in this direction by experimenting with image vectorization as an input transformation step to map the adversarial examples back into the natural manifold of MNIST handwritten digits. We compare our method vs. state-of-the-art input transformations and further discuss the trade-offs between a hand-designed and a learned transformation defense.

Knowledge transferability, or transfer learning, has been widely adopted to allow a pre-trained model in the source domain to be effectively adapted to downstream tasks in the target domain. It is thus important to explore and understand the factors affecting knowledge transferability. In this paper, as the first work, we analyze and demonstrate the connections between knowledge transferability and another important phenomenon--adversarial transferability, i.e., adversarial examples generated against one model can be transferred to attack other models. Our theoretical studies show that adversarial transferability indicates knowledge transferability and vice versa. Moreover, based on the theoretical insights, we propose two practical adversarial transferability metrics to characterize this process, serving as bidirectional indicators between adversarial and knowledge transferability. We conduct extensive experiments for different scenarios on diverse datasets, showing a positive correlation between adversarial transferability and knowledge transferability. Our findings will shed light on future research about effective knowledge transfer learning and adversarial transferability analyses.

Several machine learning models, including neural networks, consistently misclassify adversarial examples---inputs formed by applying small but intentionally worst-case perturbations to examples from the dataset, such that the perturbed input results in the model outputting an incorrect answer with high confidence. Early attempts at explaining this phenomenon focused on nonlinearity and overfitting. We argue instead that the primary cause of neural networks' vulnerability to adversarial perturbation is their linear nature. This explanation is supported by new quantitative results while giving the first explanation of the most intriguing fact about them: their generalization across architectures and training sets. Moreover, this view yields a simple and fast method of generating adversarial examples. Using this approach to provide examples for adversarial training, we reduce the test set error of a maxout network on the MNIST dataset.

Reinforcement learning from Human Feedback (RLHF) learns from preference signals, while standard Reinforcement Learning (RL) directly learns from reward signals. Preferences arguably contain less information than rewards, which makes preference-based RL seemingly more difficult. This paper theoretically proves that, for a wide range of preference models, we can solve preference-based RL directly using existing algorithms and techniques for reward-based RL, with small or no extra costs. Specifically, (1) for preferences that are drawn from reward-based probabilistic models, we reduce the problem to robust reward-based RL that can tolerate small errors in rewards; (2) for general arbitrary preferences where the objective is to find the von Neumann winner, we reduce the problem to multiagent reward-based RL which finds Nash equilibria for factored Markov games under a restricted set of policies. The latter case can be further reduce to adversarial MDP when preferences only depend on the final state. We instantiate all reward-based RL subroutines by concrete provable algorithms, and apply our theory to a large class of models including tabular MDPs and MDPs with generic function approximation. We further provide guarantees when K-wise comparisons are available.

Deep neural networks are vulnerable to adversarial examples. Adversarial training (AT) is an effective defense against adversarial examples. However, AT is prone to overfitting which degrades robustness substantially. Recently, data augmentation (DA) was shown to be effective in mitigating robust overfitting if appropriately designed and optimized for AT. This work proposes a new method to automatically learn online, instance-wise, DA policies to improve robust generalization for AT. A novel policy learning objective, consisting of Vulnerability, Affinity and Diversity, is proposed and shown to be sufficiently effective and efficient to be practical for automatic DA generation during AT. This allows our method to efficiently explore a large search space for a more effective DA policy and evolve the policy as training progresses. Empirically, our method is shown to outperform or match all competitive DA methods across various model architectures (CNNs and ViTs) and datasets (CIFAR10, SVHN and Imagenette). Our DA policy reinforced vanilla AT to surpass several state-of-the-art AT methods (with baseline DA) in terms of both accuracy and robustness. It can also be combined with those advanced AT methods to produce a further boost in robustness.

Deploying deep visual models can lead to performance drops due to the discrepancies between source and target distributions. Several approaches leverage labeled source data to estimate target domain accuracy, but accessing labeled source data is often prohibitively difficult due to data confidentiality or resource limitations on serving devices. Our work proposes a new framework to estimate model accuracy on unlabeled target data without access to source data. We investigate the feasibility of using pseudo-labels for accuracy estimation and evolve this idea into adopting recent advances in source-free domain adaptation algorithms. Our approach measures the disagreement rate between the source hypothesis and the target pseudo-labeling function, adapted from the source hypothesis. We mitigate the impact of erroneous pseudo-labels that may arise due to a high ideal joint hypothesis risk by employing adaptive adversarial perturbation on the input of the target model. Our proposed source-free framework effectively addresses the challenging distribution shift scenarios and outperforms existing methods requiring source data and labels for training.

Existing neural networks for computer vision tasks are vulnerable to adversarial attacks: adding imperceptible perturbations to the input images can fool these methods to make a false prediction on an image that was correctly predicted without the perturbation. Various defense methods have proposed image-to-image mapping methods, either including these perturbations in the training process or removing them in a preprocessing denoising step. In doing so, existing methods often ignore that the natural RGB images in today's datasets are not captured but, in fact, recovered from RAW color filter array captures that are subject to various degradations in the capture. In this work, we exploit this RAW data distribution as an empirical prior for adversarial defense. Specifically, we proposed a model-agnostic adversarial defensive method, which maps the input RGB images to Bayer RAW space and back to output RGB using a learned camera image signal processing (ISP) pipeline to eliminate potential adversarial patterns. The proposed method acts as an off-the-shelf preprocessing module and, unlike model-specific adversarial training methods, does not require adversarial images to train. As a result, the method generalizes to unseen tasks without additional retraining. Experiments on large-scale datasets (e.g., ImageNet, COCO) for different vision tasks (e.g., classification, semantic segmentation, object detection) validate that the method significantly outperforms existing methods across task domains.

With the growth of model and data sizes, a broad effort has been made to design pruning techniques that reduce the resource demand of deep learning pipelines, while retaining model performance. In order to reduce both inference and training costs, a prominent line of work uses low-rank matrix factorizations to represent the network weights. Although able to retain accuracy, we observe that low-rank methods tend to compromise model robustness against adversarial perturbations. By modeling robustness in terms of the condition number of the neural network, we argue that this loss of robustness is due to the exploding singular values of the low-rank weight matrices. Thus, we introduce a robust low-rank training algorithm that maintains the network's weights on the low-rank matrix manifold while simultaneously enforcing approximate orthonormal constraints. The resulting model reduces both training and inference costs while ensuring well-conditioning and thus better adversarial robustness, without compromising model accuracy. This is shown by extensive numerical evidence and by our main approximation theorem that shows the computed robust low-rank network well-approximates the ideal full model, provided a highly performing low-rank sub-network exists.

There is an emerging interest in generating robust counterfactual explanations that would remain valid if the model is updated or changed even slightly. Towards finding robust counterfactuals, existing literature often assumes that the original model m and the new model M are bounded in the parameter space, i.e., |Params(M){-}Params(m)|{<}Delta. However, models can often change significantly in the parameter space with little to no change in their predictions or accuracy on the given dataset. In this work, we introduce a mathematical abstraction termed naturally-occurring model change, which allows for arbitrary changes in the parameter space such that the change in predictions on points that lie on the data manifold is limited. Next, we propose a measure -- that we call Stability -- to quantify the robustness of counterfactuals to potential model changes for differentiable models, e.g., neural networks. Our main contribution is to show that counterfactuals with sufficiently high value of Stability as defined by our measure will remain valid after potential ``naturally-occurring'' model changes with high probability (leveraging concentration bounds for Lipschitz function of independent Gaussians). Since our quantification depends on the local Lipschitz constant around a data point which is not always available, we also examine practical relaxations of our proposed measure and demonstrate experimentally how they can be incorporated to find robust counterfactuals for neural networks that are close, realistic, and remain valid after potential model changes.

Neural ranking models (NRMs) have attracted considerable attention in information retrieval. Unfortunately, NRMs may inherit the adversarial vulnerabilities of general neural networks, which might be leveraged by black-hat search engine optimization practitioners. Recently, adversarial attacks against NRMs have been explored in the paired attack setting, generating an adversarial perturbation to a target document for a specific query. In this paper, we focus on a more general type of perturbation and introduce the topic-oriented adversarial ranking attack task against NRMs, which aims to find an imperceptible perturbation that can promote a target document in ranking for a group of queries with the same topic. We define both static and dynamic settings for the task and focus on decision-based black-box attacks. We propose a novel framework to improve topic-oriented attack performance based on a surrogate ranking model. The attack problem is formalized as a Markov decision process (MDP) and addressed using reinforcement learning. Specifically, a topic-oriented reward function guides the policy to find a successful adversarial example that can be promoted in rankings to as many queries as possible in a group. Experimental results demonstrate that the proposed framework can significantly outperform existing attack strategies, and we conclude by re-iterating that there exist potential risks for applying NRMs in the real world.

Single-step adversarial training (SSAT) has demonstrated the potential to achieve both efficiency and robustness. However, SSAT suffers from catastrophic overfitting (CO), a phenomenon that leads to a severely distorted classifier, making it vulnerable to multi-step adversarial attacks. In this work, we observe that some adversarial examples generated on the SSAT-trained network exhibit anomalous behaviour, that is, although these training samples are generated by the inner maximization process, their associated loss decreases instead, which we named abnormal adversarial examples (AAEs). Upon further analysis, we discover a close relationship between AAEs and classifier distortion, as both the number and outputs of AAEs undergo a significant variation with the onset of CO. Given this observation, we re-examine the SSAT process and uncover that before the occurrence of CO, the classifier already displayed a slight distortion, indicated by the presence of few AAEs. Furthermore, the classifier directly optimizing these AAEs will accelerate its distortion, and correspondingly, the variation of AAEs will sharply increase as a result. In such a vicious circle, the classifier rapidly becomes highly distorted and manifests as CO within a few iterations. These observations motivate us to eliminate CO by hindering the generation of AAEs. Specifically, we design a novel method, termed Abnormal Adversarial Examples Regularization (AAER), which explicitly regularizes the variation of AAEs to hinder the classifier from becoming distorted. Extensive experiments demonstrate that our method can effectively eliminate CO and further boost adversarial robustness with negligible additional computational overhead.

Benefiting from the message passing mechanism, Graph Neural Networks (GNNs) have been successful on flourish tasks over graph data. However, recent studies have shown that attackers can catastrophically degrade the performance of GNNs by maliciously modifying the graph structure. A straightforward solution to remedy this issue is to model the edge weights by learning a metric function between pairwise representations of two end nodes, which attempts to assign low weights to adversarial edges. The existing methods use either raw features or representations learned by supervised GNNs to model the edge weights. However, both strategies are faced with some immediate problems: raw features cannot represent various properties of nodes (e.g., structure information), and representations learned by supervised GNN may suffer from the poor performance of the classifier on the poisoned graph. We need representations that carry both feature information and as mush correct structure information as possible and are insensitive to structural perturbations. To this end, we propose an unsupervised pipeline, named STABLE, to optimize the graph structure. Finally, we input the well-refined graph into a downstream classifier. For this part, we design an advanced GCN that significantly enhances the robustness of vanilla GCN without increasing the time complexity. Extensive experiments on four real-world graph benchmarks demonstrate that STABLE outperforms the state-of-the-art methods and successfully defends against various attacks.

Deep neural networks are vulnerable to adversarial examples, dictating the imperativeness to test the model's robustness before deployment. Transfer-based attackers craft adversarial examples against surrogate models and transfer them to victim models deployed in the black-box situation. To enhance the adversarial transferability, structure-based attackers adjust the backpropagation path to avoid the attack from overfitting the surrogate model. However, existing structure-based attackers fail to explore the convolution module in CNNs and modify the backpropagation graph heuristically, leading to limited effectiveness. In this paper, we propose backPropagation pAth Search (PAS), solving the aforementioned two problems. We first propose SkipConv to adjust the backpropagation path of convolution by structural reparameterization. To overcome the drawback of heuristically designed backpropagation paths, we further construct a DAG-based search space, utilize one-step approximation for path evaluation and employ Bayesian Optimization to search for the optimal path. We conduct comprehensive experiments in a wide range of transfer settings, showing that PAS improves the attack success rate by a huge margin for both normally trained and defense models.

Recent work has demonstrated that deep neural networks are vulnerable to adversarial examples---inputs that are almost indistinguishable from natural data and yet classified incorrectly by the network. In fact, some of the latest findings suggest that the existence of adversarial attacks may be an inherent weakness of deep learning models. To address this problem, we study the adversarial robustness of neural networks through the lens of robust optimization. This approach provides us with a broad and unifying view on much of the prior work on this topic. Its principled nature also enables us to identify methods for both training and attacking neural networks that are reliable and, in a certain sense, universal. In particular, they specify a concrete security guarantee that would protect against any adversary. These methods let us train networks with significantly improved resistance to a wide range of adversarial attacks. They also suggest the notion of security against a first-order adversary as a natural and broad security guarantee. We believe that robustness against such well-defined classes of adversaries is an important stepping stone towards fully resistant deep learning models. Code and pre-trained models are available at https://github.com/MadryLab/mnist_challenge and https://github.com/MadryLab/cifar10_challenge.

The study of hardest and easiest fitness landscapes is an active area of research. Recently, Kaufmann, Larcher, Lengler and Zou conjectured that for the self-adjusting (1,lambda)-EA, Adversarial Dynamic BinVal (ADBV) is the hardest dynamic monotone function to optimize. We introduce the function Switching Dynamic BinVal (SDBV) which coincides with ADBV whenever the number of remaining zeros in the search point is strictly less than n/2, where n denotes the dimension of the search space. We show, using a combinatorial argument, that for the (1+1)-EA with any mutation rate p in [0,1], SDBV is drift-minimizing among the class of dynamic monotone functions. Our construction provides the first explicit example of an instance of the partially-ordered evolutionary algorithm (PO-EA) model with parameterized pessimism introduced by Colin, Doerr and F\'erey, building on work of Jansen. We further show that the (1+1)-EA optimizes SDBV in Theta(n^{3/2}) generations. Our simulations demonstrate matching runtimes for both static and self-adjusting (1,lambda) and (1+lambda)-EA. We further show, using an example of fixed dimension, that drift-minimization does not equal maximal runtime.

Adversarial training is well-known to produce high-quality neural network models that are empirically robust against adversarial perturbations. Nevertheless, once a model has been adversarially trained, one often desires a certification that the model is truly robust against all future attacks. Unfortunately, when faced with adversarially trained models, all existing approaches have significant trouble making certifications that are strong enough to be practically useful. Linear programming (LP) techniques in particular face a "convex relaxation barrier" that prevent them from making high-quality certifications, even after refinement with mixed-integer linear programming (MILP) and branch-and-bound (BnB) techniques. In this paper, we propose a nonconvex certification technique, based on a low-rank restriction of a semidefinite programming (SDP) relaxation. The nonconvex relaxation makes strong certifications comparable to much more expensive SDP methods, while optimizing over dramatically fewer variables comparable to much weaker LP methods. Despite nonconvexity, we show how off-the-shelf local optimization algorithms can be used to achieve and to certify global optimality in polynomial time. Our experiments find that the nonconvex relaxation almost completely closes the gap towards exact certification of adversarially trained models.

Deep neural networks are susceptible to adversarial attacks, which can compromise their performance and accuracy. Adversarial Training (AT) has emerged as a popular approach for protecting neural networks against such attacks. However, a key challenge of AT is robust overfitting, where the network's robust performance on test data deteriorates with further training, thus hindering generalization. Motivated by the concept of active forgetting in the brain, we introduce a novel learning paradigm called "Forget to Mitigate Overfitting (FOMO)". FOMO alternates between the forgetting phase, which randomly forgets a subset of weights and regulates the model's information through weight reinitialization, and the relearning phase, which emphasizes learning generalizable features. Our experiments on benchmark datasets and adversarial attacks show that FOMO alleviates robust overfitting by significantly reducing the gap between the best and last robust test accuracy while improving the state-of-the-art robustness. Furthermore, FOMO provides a better trade-off between standard and robust accuracy, outperforming baseline adversarial methods. Finally, our framework is robust to AutoAttacks and increases generalization in many real-world scenarios.

Recent research has revealed that the output of Deep Neural Networks (DNN) can be easily altered by adding relatively small perturbations to the input vector. In this paper, we analyze an attack in an extremely limited scenario where only one pixel can be modified. For that we propose a novel method for generating one-pixel adversarial perturbations based on differential evolution (DE). It requires less adversarial information (a black-box attack) and can fool more types of networks due to the inherent features of DE. The results show that 67.97% of the natural images in Kaggle CIFAR-10 test dataset and 16.04% of the ImageNet (ILSVRC 2012) test images can be perturbed to at least one target class by modifying just one pixel with 74.03% and 22.91% confidence on average. We also show the same vulnerability on the original CIFAR-10 dataset. Thus, the proposed attack explores a different take on adversarial machine learning in an extreme limited scenario, showing that current DNNs are also vulnerable to such low dimension attacks. Besides, we also illustrate an important application of DE (or broadly speaking, evolutionary computation) in the domain of adversarial machine learning: creating tools that can effectively generate low-cost adversarial attacks against neural networks for evaluating robustness.

The trade-off between robustness and accuracy has been widely studied in the adversarial literature. Although still controversial, the prevailing view is that this trade-off is inherent, either empirically or theoretically. Thus, we dig for the origin of this trade-off in adversarial training and find that it may stem from the improperly defined robust error, which imposes an inductive bias of local invariance -- an overcorrection towards smoothness. Given this, we advocate employing local equivariance to describe the ideal behavior of a robust model, leading to a self-consistent robust error named SCORE. By definition, SCORE facilitates the reconciliation between robustness and accuracy, while still handling the worst-case uncertainty via robust optimization. By simply substituting KL divergence with variants of distance metrics, SCORE can be efficiently minimized. Empirically, our models achieve top-rank performance on RobustBench under AutoAttack. Besides, SCORE provides instructive insights for explaining the overfitting phenomenon and semantic input gradients observed on robust models. Code is available at https://github.com/P2333/SCORE.

We propose the first loss function for approximate Nash equilibria of normal-form games that is amenable to unbiased Monte Carlo estimation. This construction allows us to deploy standard non-convex stochastic optimization techniques for approximating Nash equilibria, resulting in novel algorithms with provable guarantees. We complement our theoretical analysis with experiments demonstrating that stochastic gradient descent can outperform previous state-of-the-art approaches.

Differentially private (DP) optimization is the standard paradigm to learn large neural networks that are accurate and privacy-preserving. The computational cost for DP deep learning, however, is notoriously heavy due to the per-sample gradient clipping. Existing DP implementations are 2-1000times more costly in time and space complexity than the standard (non-private) training. In this work, we develop a novel Book-Keeping (BK) technique that implements existing DP optimizers (thus achieving the same accuracy), with a substantial improvement on the computational cost. Specifically, BK enables DP training on large models and high dimensional data to be roughly as efficient as the standard training, whereas previous DP algorithms can be inefficient or incapable of training due to memory error. The computational advantage of BK is supported by the complexity analysis as well as extensive experiments on vision and language tasks. Our implementation achieves state-of-the-art (SOTA) accuracy with very small extra cost: on GPT2 and at the same memory cost, BK has 1.0times the time complexity of the standard training (0.75times training speed in practice), and 0.6times the time complexity of the most efficient DP implementation (1.24times training speed in practice). We will open-source the codebase for the BK algorithm.

The vulnerability of deep neural networks to adversarial patches has motivated numerous defense strategies for boosting model robustness. However, the prevailing defenses depend on single observation or pre-established adversary information to counter adversarial patches, often failing to be confronted with unseen or adaptive adversarial attacks and easily exhibiting unsatisfying performance in dynamic 3D environments. Inspired by active human perception and recurrent feedback mechanisms, we develop Embodied Active Defense (EAD), a proactive defensive strategy that actively contextualizes environmental information to address misaligned adversarial patches in 3D real-world settings. To achieve this, EAD develops two central recurrent sub-modules, i.e., a perception module and a policy module, to implement two critical functions of active vision. These models recurrently process a series of beliefs and observations, facilitating progressive refinement of their comprehension of the target object and enabling the development of strategic actions to counter adversarial patches in 3D environments. To optimize learning efficiency, we incorporate a differentiable approximation of environmental dynamics and deploy patches that are agnostic to the adversary strategies. Extensive experiments demonstrate that EAD substantially enhances robustness against a variety of patches within just a few steps through its action policy in safety-critical tasks (e.g., face recognition and object detection), without compromising standard accuracy. Furthermore, due to the attack-agnostic characteristic, EAD facilitates excellent generalization to unseen attacks, diminishing the averaged attack success rate by 95 percent across a range of unseen adversarial attacks.

Perceptual similarity metrics have progressively become more correlated with human judgments on perceptual similarity; however, despite recent advances, the addition of an imperceptible distortion can still compromise these metrics. In our study, we systematically examine the robustness of these metrics to imperceptible adversarial perturbations. Following the two-alternative forced-choice experimental design with two distorted images and one reference image, we perturb the distorted image closer to the reference via an adversarial attack until the metric flips its judgment. We first show that all metrics in our study are susceptible to perturbations generated via common adversarial attacks such as FGSM, PGD, and the One-pixel attack. Next, we attack the widely adopted LPIPS metric using spatial-transformation-based adversarial perturbations (stAdv) in a white-box setting to craft adversarial examples that can effectively transfer to other similarity metrics in a black-box setting. We also combine the spatial attack stAdv with PGD (ell_infty-bounded) attack to increase transferability and use these adversarial examples to benchmark the robustness of both traditional and recently developed metrics. Our benchmark provides a good starting point for discussion and further research on the robustness of metrics to imperceptible adversarial perturbations.

We propose a game-based formulation for learning dimensionality-reducing representations of feature vectors, when only a prior knowledge on future prediction tasks is available. In this game, the first player chooses a representation, and then the second player adversarially chooses a prediction task from a given class, representing the prior knowledge. The first player aims is to minimize, and the second player to maximize, the regret: The minimal prediction loss using the representation, compared to the same loss using the original features. For the canonical setting in which the representation, the response to predict and the predictors are all linear functions, and under the mean squared error loss function, we derive the theoretically optimal representation in pure strategies, which shows the effectiveness of the prior knowledge, and the optimal regret in mixed strategies, which shows the usefulness of randomizing the representation. For general representations and loss functions, we propose an efficient algorithm to optimize a randomized representation. The algorithm only requires the gradients of the loss function, and is based on incrementally adding a representation rule to a mixture of such rules.

Adversarial training is exploited to develop a robust Deep Neural Network (DNN) model against the malicious altered data. These attacks may have catastrophic effects on DNN models but are indistinguishable for a human being. For example, an external attack can modify an image adding noises invisible for a human eye, but a DNN model misclassified the image. A key objective for developing robust DNN models is to use a learning algorithm that is fast but can also give model that is robust against different types of adversarial attacks. Especially for adversarial training, enormously long training times are needed for obtaining high accuracy under many different types of adversarial samples generated using different adversarial attack techniques. This paper aims at accelerating the adversarial training to enable fast development of robust DNN models against adversarial attacks. The general method for improving the training performance is the hyperparameters fine-tuning, where the learning rate is one of the most crucial hyperparameters. By modifying its shape (the value over time) and value during the training, we can obtain a model robust to adversarial attacks faster than standard training. First, we conduct experiments on two different datasets (CIFAR10, CIFAR100), exploring various techniques. Then, this analysis is leveraged to develop a novel fast training methodology, AccelAT, which automatically adjusts the learning rate for different epochs based on the accuracy gradient. The experiments show comparable results with the related works, and in several experiments, the adversarial training of DNNs using our AccelAT framework is conducted up to 2 times faster than the existing techniques. Thus, our findings boost the speed of adversarial training in an era in which security and performance are fundamental optimization objectives in DNN-based applications.

Conditional computing processes an input using only part of the neural network's computational units. Learning to execute parts of a deep convolutional network by routing individual samples has several advantages: Reducing the computational burden is an obvious advantage. Furthermore, if similar classes are routed to the same path, that part of the network learns to discriminate between finer differences and better classification accuracies can be attained with fewer parameters. Recently, several papers have exploited this idea to take a particular child of a node in a tree-shaped network or to skip parts of a network. In this work, we follow a Trellis-based approach for generating specific execution paths in a deep convolutional neural network. We have designed routing mechanisms that use differentiable information gain-based cost functions to determine which subset of features in a convolutional layer will be executed. We call our method Conditional Information Gain Trellis (CIGT). We show that our conditional execution mechanism achieves comparable or better model performance compared to unconditional baselines, using only a fraction of the computational resources.

Traditional white-box methods for creating adversarial perturbations against LLMs typically rely only on gradient computation from the targeted model, ignoring the internal mechanisms responsible for attack success or failure. Conversely, interpretability studies that analyze these internal mechanisms lack practical applications beyond runtime interventions. We bridge this gap by introducing a novel white-box approach that leverages mechanistic interpretability techniques to craft practical adversarial inputs. Specifically, we first identify acceptance subspaces - sets of feature vectors that do not trigger the model's refusal mechanisms - then use gradient-based optimization to reroute embeddings from refusal subspaces to acceptance subspaces, effectively achieving jailbreaks. This targeted approach significantly reduces computation cost, achieving attack success rates of 80-95\% on state-of-the-art models including Gemma2, Llama3.2, and Qwen2.5 within minutes or even seconds, compared to existing techniques that often fail or require hours of computation. We believe this approach opens a new direction for both attack research and defense development. Furthermore, it showcases a practical application of mechanistic interpretability where other methods are less efficient, which highlights its utility. The code and generated datasets are available at https://github.com/Sckathach/subspace-rerouting.

Optimization problems with nonlinear cost functions and combinatorial constraints appear in many real-world applications but remain challenging to solve efficiently compared to their linear counterparts. To bridge this gap, we propose SurCo that learns linear text{Sur}rogate costs which can be used in existing text{Co}mbinatorial solvers to output good solutions to the original nonlinear combinatorial optimization problem. The surrogate costs are learned end-to-end with nonlinear loss by differentiating through the linear surrogate solver, combining the flexibility of gradient-based methods with the structure of linear combinatorial optimization. We propose three SurCo variants: SurCo-zero for individual nonlinear problems, SurCo-prior for problem distributions, and SurCo-hybrid to combine both distribution and problem-specific information. We give theoretical intuition motivating SurCo, and evaluate it empirically. Experiments show that SurCo finds better solutions faster than state-of-the-art and domain expert approaches in real-world optimization problems such as embedding table sharding, inverse photonic design, and nonlinear route planning.

Adversarial training improves the robustness of neural networks against adversarial attacks, albeit at the expense of the trade-off between standard and robust generalization. To unveil the underlying factors driving this phenomenon, we examine the layer-wise learning capabilities of neural networks during the transition from a standard to an adversarial setting. Our empirical findings demonstrate that selectively updating specific layers while preserving others can substantially enhance the network's learning capacity. We therefore propose CURE, a novel training framework that leverages a gradient prominence criterion to perform selective conservation, updating, and revision of weights. Importantly, CURE is designed to be dataset- and architecture-agnostic, ensuring its applicability across various scenarios. It effectively tackles both memorization and overfitting issues, thus enhancing the trade-off between robustness and generalization and additionally, this training approach also aids in mitigating "robust overfitting". Furthermore, our study provides valuable insights into the mechanisms of selective adversarial training and offers a promising avenue for future research.

In this paper, we propose a novel adversarial defence mechanism for image classification -- CARSO -- inspired by cues from cognitive neuroscience. The method is synergistically complementary to adversarial training and relies on knowledge of the internal representation of the attacked classifier. Exploiting a generative model for adversarial purification, conditioned on such representation, it samples reconstructions of inputs to be finally classified. Experimental evaluation by a well-established benchmark of varied, strong adaptive attacks, across diverse image datasets and classifier architectures, shows that CARSO is able to defend the classifier significantly better than state-of-the-art adversarial training alone -- with a tolerable clean accuracy toll. Furthermore, the defensive architecture succeeds in effectively shielding itself from unforeseen threats, and end-to-end attacks adapted to fool stochastic defences. Code and pre-trained models are available at https://github.com/emaballarin/CARSO .

We extend conformal prediction to control the expected value of any monotone loss function. The algorithm generalizes split conformal prediction together with its coverage guarantee. Like conformal prediction, the conformal risk control procedure is tight up to an O(1/n) factor. We also introduce extensions of the idea to distribution shift, quantile risk control, multiple and adversarial risk control, and expectations of U-statistics. Worked examples from computer vision and natural language processing demonstrate the usage of our algorithm to bound the false negative rate, graph distance, and token-level F1-score.

Loss functions serve as the foundation of supervised learning and are often chosen prior to model development. To avoid potentially ad hoc choices of losses, statistical decision theory describes a desirable property for losses known as properness, which asserts that Bayes' rule is optimal. Recent works have sought to learn losses and models jointly. Existing methods do this by fitting an inverse canonical link function which monotonically maps R to [0,1] to estimate probabilities for binary problems. In this paper, we extend monotonicity to maps between R^{C-1} and the projected probability simplex Delta^{C-1} by using monotonicity of gradients of convex functions. We present {\sc LegendreTron} as a novel and practical method that jointly learns proper canonical losses and probabilities for multiclass problems. Tested on a benchmark of domains with up to 1,000 classes, our experimental results show that our method consistently outperforms the natural multiclass baseline under a t-test at 99% significance on all datasets with greater than 10 classes.

Recent studies have shown that episodic reinforcement learning (RL) is no harder than bandits when the total reward is bounded by 1, and proved regret bounds that have a polylogarithmic dependence on the planning horizon H. However, it remains an open question that if such results can be carried over to adversarial RL, where the reward is adversarially chosen at each episode. In this paper, we answer this question affirmatively by proposing the first horizon-free policy search algorithm. To tackle the challenges caused by exploration and adversarially chosen reward, our algorithm employs (1) a variance-uncertainty-aware weighted least square estimator for the transition kernel; and (2) an occupancy measure-based technique for the online search of a stochastic policy. We show that our algorithm achieves an Obig((d+log (|S|^2 |A|))Kbig) regret with full-information feedback, where d is the dimension of a known feature mapping linearly parametrizing the unknown transition kernel of the MDP, K is the number of episodes, |S| and |A| are the cardinalities of the state and action spaces. We also provide hardness results and regret lower bounds to justify the near optimality of our algorithm and the unavoidability of log|S| and log|A| in the regret bound.

It is typically understood that the training of modern neural networks is a process of fitting the probability distribution of desired output. However, recent paradoxical observations in a number of language generation tasks let one wonder if this canonical probability-based explanation can really account for the empirical success of deep learning. To resolve this issue, we propose an alternative utility-based explanation to the standard supervised learning procedure in deep learning. The basic idea is to interpret the learned neural network not as a probability model but as an ordinal utility function that encodes the preference revealed in training data. In this perspective, training of the neural network corresponds to a utility learning process. Specifically, we show that for all neural networks with softmax outputs, the SGD learning dynamic of maximum likelihood estimation (MLE) can be seen as an iteration process that optimizes the neural network toward an optimal utility function. This utility-based interpretation can explain several otherwise-paradoxical observations about the neural networks thus trained. Moreover, our utility-based theory also entails an equation that can transform the learned utility values back to a new kind of probability estimation with which probability-compatible decision rules enjoy dramatic (double-digits) performance improvements. These evidences collectively reveal a phenomenon of utility-probability duality in terms of what modern neural networks are (truly) modeling: We thought they are one thing (probabilities), until the unexplainable showed up; changing mindset and treating them as another thing (utility values) largely reconcile the theory, despite remaining subtleties regarding its original (probabilistic) identity.

Meta-gradient Reinforcement Learning (RL) allows agents to self-tune their hyper-parameters in an online fashion during training. In this paper, we identify a bias in the meta-gradient of current meta-gradient RL approaches. This bias comes from using the critic that is trained using the meta-learned discount factor for the advantage estimation in the outer objective which requires a different discount factor. Because the meta-learned discount factor is typically lower than the one used in the outer objective, the resulting bias can cause the meta-gradient to favor myopic policies. We propose a simple solution to this issue: we eliminate this bias by using an alternative, outer value function in the estimation of the outer loss. To obtain this outer value function we add a second head to the critic network and train it alongside the classic critic, using the outer loss discount factor. On an illustrative toy problem, we show that the bias can cause catastrophic failure of current meta-gradient RL approaches, and show that our proposed solution fixes it. We then apply our method to a more complex environment and demonstrate that fixing the meta-gradient bias can significantly improve performance.

Recent studies have shown that robustness to adversarial attacks can be transferred across networks. In other words, we can make a weak model more robust with the help of a strong teacher model. We ask if instead of learning from a static teacher, can models "learn together" and "teach each other" to achieve better robustness? In this paper, we study how interactions among models affect robustness via knowledge distillation. We propose mutual adversarial training (MAT), in which multiple models are trained together and share the knowledge of adversarial examples to achieve improved robustness. MAT allows robust models to explore a larger space of adversarial samples, and find more robust feature spaces and decision boundaries. Through extensive experiments on CIFAR-10 and CIFAR-100, we demonstrate that MAT can effectively improve model robustness and outperform state-of-the-art methods under white-box attacks, bringing sim8% accuracy gain to vanilla adversarial training (AT) under PGD-100 attacks. In addition, we show that MAT can also mitigate the robustness trade-off among different perturbation types, bringing as much as 13.1% accuracy gain to AT baselines against the union of l_infty, l_2 and l_1 attacks. These results show the superiority of the proposed method and demonstrate that collaborative learning is an effective strategy for designing robust models.

Adversarial attacks have been a looming and unaddressed threat in the industry. However, through a decade-long history of the robustness evaluation literature, we have learned that mounting a strong or optimal attack is challenging. It requires both machine learning and domain expertise. In other words, the white-box threat model, religiously assumed by a large majority of the past literature, is unrealistic. In this paper, we propose a new practical threat model where the adversary relies on transfer attacks through publicly available surrogate models. We argue that this setting will become the most prevalent for security-sensitive applications in the future. We evaluate the transfer attacks in this setting and propose a specialized defense method based on a game-theoretic perspective. The defenses are evaluated under 24 public models and 11 attack algorithms across three datasets (CIFAR-10, CIFAR-100, and ImageNet). Under this threat model, our defense, PubDef, outperforms the state-of-the-art white-box adversarial training by a large margin with almost no loss in the normal accuracy. For instance, on ImageNet, our defense achieves 62% accuracy under the strongest transfer attack vs only 36% of the best adversarially trained model. Its accuracy when not under attack is only 2% lower than that of an undefended model (78% vs 80%). We release our code at https://github.com/wagner-group/pubdef.

Understanding and analyzing markets is crucial, yet analytical equilibrium solutions remain largely infeasible. Recent breakthroughs in equilibrium computation rely on zeroth-order policy gradient estimation. These approaches commonly suffer from high variance and are computationally expensive. The use of fully differentiable simulators would enable more efficient gradient estimation. However, the discrete allocation of goods in economic simulations is a non-differentiable operation. This renders the first-order Monte Carlo gradient estimator inapplicable and the learning feedback systematically misleading. We propose a novel smoothing technique that creates a surrogate market game, in which first-order methods can be applied. We provide theoretical bounds on the resulting bias which justifies solving the smoothed game instead. These bounds also allow choosing the smoothing strength a priori such that the resulting estimate has low variance. Furthermore, we validate our approach via numerous empirical experiments. Our method theoretically and empirically outperforms zeroth-order methods in approximation quality and computational efficiency.

Representation learning methods have revolutionized machine learning on networks by converting discrete network structures into continuous domains. However, dynamic networks that evolve over time pose new challenges. To address this, dynamic representation learning methods have gained attention, offering benefits like reduced learning time and improved accuracy by utilizing temporal information. T-batching is a valuable technique for training dynamic network models that reduces training time while preserving vital conditions for accurate modeling. However, we have identified a limitation in the training loss function used with t-batching. Through mathematical analysis, we propose two alternative loss functions that overcome these issues, resulting in enhanced training performance. We extensively evaluate the proposed loss functions on synthetic and real-world dynamic networks. The results consistently demonstrate superior performance compared to the original loss function. Notably, in a real-world network characterized by diverse user interaction histories, the proposed loss functions achieved more than 26.9% enhancement in Mean Reciprocal Rank (MRR) and more than 11.8% improvement in Recall@10. These findings underscore the efficacy of the proposed loss functions in dynamic network modeling.

Deep neural networks have been shown to be susceptible to adversarial examples -- small, imperceptible changes constructed to cause mis-classification in otherwise highly accurate image classifiers. As a practical alternative, recent work proposed so-called adversarial patches: clearly visible, but adversarially crafted rectangular patches in images. These patches can easily be printed and applied in the physical world. While defenses against imperceptible adversarial examples have been studied extensively, robustness against adversarial patches is poorly understood. In this work, we first devise a practical approach to obtain adversarial patches while actively optimizing their location within the image. Then, we apply adversarial training on these location-optimized adversarial patches and demonstrate significantly improved robustness on CIFAR10 and GTSRB. Additionally, in contrast to adversarial training on imperceptible adversarial examples, our adversarial patch training does not reduce accuracy.

Adversarial training, which is to enhance robustness against adversarial attacks, has received much attention because it is easy to generate human-imperceptible perturbations of data to deceive a given deep neural network. In this paper, we propose a new adversarial training algorithm that is theoretically well motivated and empirically superior to other existing algorithms. A novel feature of the proposed algorithm is to apply more regularization to data vulnerable to adversarial attacks than other existing regularization algorithms do. Theoretically, we show that our algorithm can be understood as an algorithm of minimizing the regularized empirical risk motivated from a newly derived upper bound of the robust risk. Numerical experiments illustrate that our proposed algorithm improves the generalization (accuracy on examples) and robustness (accuracy on adversarial attacks) simultaneously to achieve the state-of-the-art performance.

This paper investigates the problem of ensembling multiple strategies for sequential portfolios to outperform individual strategies in terms of long-term wealth. Due to the uncertainty of strategies' performances in the future market, which are often based on specific models and statistical assumptions, investors often mitigate risk and enhance robustness by combining multiple strategies, akin to common approaches in collective learning prediction. However, the absence of a distribution-free and consistent preference framework complicates decisions of combination due to the ambiguous objective. To address this gap, we introduce a novel framework for decision-making in combining strategies, irrespective of market conditions, by establishing the investor's preference between decisions and then forming a clear objective. Through this framework, we propose a combinatorial strategy construction, free from statistical assumptions, for any scale of component strategies, even infinite, such that it meets the determined criterion. Finally, we test the proposed strategy along with its accelerated variant and some other multi-strategies. The numerical experiments show results in favor of the proposed strategies, albeit with small tradeoffs in their Sharpe ratios, in which their cumulative wealths eventually exceed those of the best component strategies while the accelerated strategy significantly improves performance.

Recently, Diffusion Models (DMs) boost a wave in AI for Art yet raise new copyright concerns, where infringers benefit from using unauthorized paintings to train DMs to generate novel paintings in a similar style. To address these emerging copyright violations, in this paper, we are the first to explore and propose to utilize adversarial examples for DMs to protect human-created artworks. Specifically, we first build a theoretical framework to define and evaluate the adversarial examples for DMs. Then, based on this framework, we design a novel algorithm, named AdvDM, which exploits a Monte-Carlo estimation of adversarial examples for DMs by optimizing upon different latent variables sampled from the reverse process of DMs. Extensive experiments show that the generated adversarial examples can effectively hinder DMs from extracting their features. Therefore, our method can be a powerful tool for human artists to protect their copyright against infringers equipped with DM-based AI-for-Art applications. The code of our method is available on GitHub: https://github.com/mist-project/mist.git.

We focus on the problem of black-box adversarial attacks, where the aim is to generate adversarial examples for deep learning models solely based on information limited to output label~(hard label) to a queried data input. We propose a simple and efficient Bayesian Optimization~(BO) based approach for developing black-box adversarial attacks. Issues with BO's performance in high dimensions are avoided by searching for adversarial examples in a structured low-dimensional subspace. We demonstrate the efficacy of our proposed attack method by evaluating both ell_infty and ell_2 norm constrained untargeted and targeted hard label black-box attacks on three standard datasets - MNIST, CIFAR-10 and ImageNet. Our proposed approach consistently achieves 2x to 10x higher attack success rate while requiring 10x to 20x fewer queries compared to the current state-of-the-art black-box adversarial attacks.

Forward Gradients - the idea of using directional derivatives in forward differentiation mode - have recently been shown to be utilizable for neural network training while avoiding problems generally associated with backpropagation gradient computation, such as locking and memorization requirements. The cost is the requirement to guess the step direction, which is hard in high dimensions. While current solutions rely on weighted averages over isotropic guess vector distributions, we propose to strongly bias our gradient guesses in directions that are much more promising, such as feedback obtained from small, local auxiliary networks. For a standard computer vision neural network, we conduct a rigorous study systematically covering a variety of combinations of gradient targets and gradient guesses, including those previously presented in the literature. We find that using gradients obtained from a local loss as a candidate direction drastically improves on random noise in Forward Gradient methods.

Deep hedging is a promising direction in quantitative finance, incorporating models and techniques from deep learning research. While giving excellent hedging strategies, models inherently requires careful treatment in designing architectures for neural networks. To mitigate such difficulties, we introduce SigFormer, a novel deep learning model that combines the power of path signatures and transformers to handle sequential data, particularly in cases with irregularities. Path signatures effectively capture complex data patterns, while transformers provide superior sequential attention. Our proposed model is empirically compared to existing methods on synthetic data, showcasing faster learning and enhanced robustness, especially in the presence of irregular underlying price data. Additionally, we validate our model performance through a real-world backtest on hedging the SP 500 index, demonstrating positive outcomes.

While the transferability property of adversarial examples allows the adversary to perform black-box attacks (i.e., the attacker has no knowledge about the target model), the transfer-based adversarial attacks have gained great attention. Previous works mostly study gradient variation or image transformations to amplify the distortion on critical parts of inputs. These methods can work on transferring across models with limited differences, i.e., from CNNs to CNNs, but always fail in transferring across models with wide differences, such as from CNNs to ViTs. Alternatively, model ensemble adversarial attacks are proposed to fuse outputs from surrogate models with diverse architectures to get an ensemble loss, making the generated adversarial example more likely to transfer to other models as it can fool multiple models concurrently. However, existing ensemble attacks simply fuse the outputs of the surrogate models evenly, thus are not efficacious to capture and amplify the intrinsic transfer information of adversarial examples. In this paper, we propose an adaptive ensemble attack, dubbed AdaEA, to adaptively control the fusion of the outputs from each model, via monitoring the discrepancy ratio of their contributions towards the adversarial objective. Furthermore, an extra disparity-reduced filter is introduced to further synchronize the update direction. As a result, we achieve considerable improvement over the existing ensemble attacks on various datasets, and the proposed AdaEA can also boost existing transfer-based attacks, which further demonstrates its efficacy and versatility.

Bayesian inference usually requires running potentially costly inference procedures separately for every new observation. In contrast, the idea of amortized Bayesian inference is to initially invest computational cost in training an inference network on simulated data, which can subsequently be used to rapidly perform inference (i.e., to return estimates of posterior distributions) for new observations. This approach has been applied to many real-world models in the sciences and engineering, but it is unclear how robust the approach is to adversarial perturbations in the observed data. Here, we study the adversarial robustness of amortized Bayesian inference, focusing on simulation-based estimation of multi-dimensional posterior distributions. We show that almost unrecognizable, targeted perturbations of the observations can lead to drastic changes in the predicted posterior and highly unrealistic posterior predictive samples, across several benchmark tasks and a real-world example from neuroscience. We propose a computationally efficient regularization scheme based on penalizing the Fisher information of the conditional density estimator, and show how it improves the adversarial robustness of amortized Bayesian inference.

Despite their tremendous success in modelling high-dimensional data manifolds, deep neural networks suffer from the threat of adversarial attacks - Existence of perceptually valid input-like samples obtained through careful perturbation that lead to degradation in the performance of the underlying model. Major concerns with existing defense mechanisms include non-generalizability across different attacks, models and large inference time. In this paper, we propose a generalized defense mechanism capitalizing on the expressive power of regularized latent space based generative models. We design an adversarial filter, devoid of access to classifier and adversaries, which makes it usable in tandem with any classifier. The basic idea is to learn a Lipschitz constrained mapping from the data manifold, incorporating adversarial perturbations, to a quantized latent space and re-map it to the true data manifold. Specifically, we simultaneously auto-encode the data manifold and its perturbations implicitly through the perturbations of the regularized and quantized generative latent space, realized using variational inference. We demonstrate the efficacy of the proposed formulation in providing resilience against multiple attack types (black and white box) and methods, while being almost real-time. Our experiments show that the proposed method surpasses the state-of-the-art techniques in several cases.

Generalizing policies across different domains with dynamics mismatch poses a significant challenge in reinforcement learning. For example, a robot learns the policy in a simulator, but when it is deployed in the real world, the dynamics of the environment may be different. Given the source and target domain with dynamics mismatch, we consider the online dynamics adaptation problem, in which case the agent can access sufficient source domain data while online interactions with the target domain are limited. Existing research has attempted to solve the problem from the dynamics discrepancy perspective. In this work, we reveal the limitations of these methods and explore the problem from the value difference perspective via a novel insight on the value consistency across domains. Specifically, we present the Value-Guided Data Filtering (VGDF) algorithm, which selectively shares transitions from the source domain based on the proximity of paired value targets across the two domains. Empirical results on various environments with kinematic and morphology shifts demonstrate that our method achieves superior performance compared to prior approaches.

In this work, we leverage visual prompting (VP) to improve adversarial robustness of a fixed, pre-trained model at testing time. Compared to conventional adversarial defenses, VP allows us to design universal (i.e., data-agnostic) input prompting templates, which have plug-and-play capabilities at testing time to achieve desired model performance without introducing much computation overhead. Although VP has been successfully applied to improving model generalization, it remains elusive whether and how it can be used to defend against adversarial attacks. We investigate this problem and show that the vanilla VP approach is not effective in adversarial defense since a universal input prompt lacks the capacity for robust learning against sample-specific adversarial perturbations. To circumvent it, we propose a new VP method, termed Class-wise Adversarial Visual Prompting (C-AVP), to generate class-wise visual prompts so as to not only leverage the strengths of ensemble prompts but also optimize their interrelations to improve model robustness. Our experiments show that C-AVP outperforms the conventional VP method, with 2.1X standard accuracy gain and 2X robust accuracy gain. Compared to classical test-time defenses, C-AVP also yields a 42X inference time speedup.

We investigate the problem of stochastic, combinatorial multi-armed bandits where the learner only has access to bandit feedback and the reward function can be non-linear. We provide a general framework for adapting discrete offline approximation algorithms into sublinear alpha-regret methods that only require bandit feedback, achieving Oleft(T^2{3}log(T)^1{3}right) expected cumulative alpha-regret dependence on the horizon T. The framework only requires the offline algorithms to be robust to small errors in function evaluation. The adaptation procedure does not even require explicit knowledge of the offline approximation algorithm -- the offline algorithm can be used as black box subroutine. To demonstrate the utility of the proposed framework, the proposed framework is applied to multiple problems in submodular maximization, adapting approximation algorithms for cardinality and for knapsack constraints. The new CMAB algorithms for knapsack constraints outperform a full-bandit method developed for the adversarial setting in experiments with real-world data.

Despite the success of convolutional neural networks (CNNs) in many academic benchmarks for computer vision tasks, their application in the real-world is still facing fundamental challenges. One of these open problems is the inherent lack of robustness, unveiled by the striking effectiveness of adversarial attacks. Current attack methods are able to manipulate the network's prediction by adding specific but small amounts of noise to the input. In turn, adversarial training (AT) aims to achieve robustness against such attacks and ideally a better model generalization ability by including adversarial samples in the trainingset. However, an in-depth analysis of the resulting robust models beyond adversarial robustness is still pending. In this paper, we empirically analyze a variety of adversarially trained models that achieve high robust accuracies when facing state-of-the-art attacks and we show that AT has an interesting side-effect: it leads to models that are significantly less overconfident with their decisions, even on clean data than non-robust models. Further, our analysis of robust models shows that not only AT but also the model's building blocks (like activation functions and pooling) have a strong influence on the models' prediction confidences. Data & Project website: https://github.com/GeJulia/robustness_confidences_evaluation

We propose transferability from Large Geometric Vicinity (LGV), a new technique to increase the transferability of black-box adversarial attacks. LGV starts from a pretrained surrogate model and collects multiple weight sets from a few additional training epochs with a constant and high learning rate. LGV exploits two geometric properties that we relate to transferability. First, models that belong to a wider weight optimum are better surrogates. Second, we identify a subspace able to generate an effective surrogate ensemble among this wider optimum. Through extensive experiments, we show that LGV alone outperforms all (combinations of) four established test-time transformations by 1.8 to 59.9 percentage points. Our findings shed new light on the importance of the geometry of the weight space to explain the transferability of adversarial examples.

Modern representation learning methods often struggle to adapt quickly under non-stationarity because they suffer from catastrophic forgetting and decaying plasticity. Such problems prevent learners from fast adaptation since they may forget useful features or have difficulty learning new ones. Hence, these methods are rendered ineffective for continual learning. This paper proposes Utility-based Perturbed Gradient Descent (UPGD), an online learning algorithm well-suited for continual learning agents. UPGD protects useful weights or features from forgetting and perturbs less useful ones based on their utilities. Our empirical results show that UPGD helps reduce forgetting and maintain plasticity, enabling modern representation learning methods to work effectively in continual learning.

Adversarial examples provoke weak reliability and potential security issues in deep neural networks. Although adversarial training has been widely studied to improve adversarial robustness, it works in an over-parameterized regime and requires high computations and large memory budgets. To bridge adversarial robustness and model compression, we propose a novel adversarial pruning method, Masking Adversarial Damage (MAD) that employs second-order information of adversarial loss. By using it, we can accurately estimate adversarial saliency for model parameters and determine which parameters can be pruned without weakening adversarial robustness. Furthermore, we reveal that model parameters of initial layer are highly sensitive to the adversarial examples and show that compressed feature representation retains semantic information for the target objects. Through extensive experiments on three public datasets, we demonstrate that MAD effectively prunes adversarially trained networks without loosing adversarial robustness and shows better performance than previous adversarial pruning methods.

The conventional wisdom behind learning deep classification models is to focus on bad-classified examples and ignore well-classified examples that are far from the decision boundary. For instance, when training with cross-entropy loss, examples with higher likelihoods (i.e., well-classified examples) contribute smaller gradients in back-propagation. However, we theoretically show that this common practice hinders representation learning, energy optimization, and margin growth. To counteract this deficiency, we propose to reward well-classified examples with additive bonuses to revive their contribution to the learning process. This counterexample theoretically addresses these three issues. We empirically support this claim by directly verifying the theoretical results or significant performance improvement with our counterexample on diverse tasks, including image classification, graph classification, and machine translation. Furthermore, this paper shows that we can deal with complex scenarios, such as imbalanced classification, OOD detection, and applications under adversarial attacks because our idea can solve these three issues. Code is available at: https://github.com/lancopku/well-classified-examples-are-underestimated.

Recommender systems play a pivotal role in mitigating information overload in various fields. Nonetheless, the inherent openness of these systems introduces vulnerabilities, allowing attackers to insert fake users into the system's training data to skew the exposure of certain items, known as poisoning attacks. Adversarial training has emerged as a notable defense mechanism against such poisoning attacks within recommender systems. Existing adversarial training methods apply perturbations of the same magnitude across all users to enhance system robustness against attacks. Yet, in reality, we find that attacks often affect only a subset of users who are vulnerable. These perturbations of indiscriminate magnitude make it difficult to balance effective protection for vulnerable users without degrading recommendation quality for those who are not affected. To address this issue, our research delves into understanding user vulnerability. Considering that poisoning attacks pollute the training data, we note that the higher degree to which a recommender system fits users' training data correlates with an increased likelihood of users incorporating attack information, indicating their vulnerability. Leveraging these insights, we introduce the Vulnerability-aware Adversarial Training (VAT), designed to defend against poisoning attacks in recommender systems. VAT employs a novel vulnerability-aware function to estimate users' vulnerability based on the degree to which the system fits them. Guided by this estimation, VAT applies perturbations of adaptive magnitude to each user, not only reducing the success ratio of attacks but also preserving, and potentially enhancing, the quality of recommendations. Comprehensive experiments confirm VAT's superior defensive capabilities across different recommendation models and against various types of attacks.

Multiplications are responsible for most of the computational cost involved in neural network training and inference. Recent research has thus looked for ways to reduce the cost associated with them. Inspired by Mogami (2020), we replace multiplication with a cheap piecewise affine approximation that is achieved by adding the bit representation of the floating point numbers together as integers. We show that transformers can be trained with the resulting modified matrix multiplications on both vision and language tasks with little to no performance impact, and without changes to the training hyperparameters. We further replace all non-linearities in the networks making them fully and jointly piecewise affine in both inputs and weights. Finally, we show that we can eliminate all multiplications in the entire training process, including operations in the forward pass, backward pass and optimizer update, demonstrating the first successful training of modern neural network architectures in a fully multiplication-free fashion.

Normalization layers and activation functions are fundamental components in deep networks and typically co-locate with each other. Here we propose to design them using an automated approach. Instead of designing them separately, we unify them into a single tensor-to-tensor computation graph, and evolve its structure starting from basic mathematical functions. Examples of such mathematical functions are addition, multiplication and statistical moments. The use of low-level mathematical functions, in contrast to the use of high-level modules in mainstream NAS, leads to a highly sparse and large search space which can be challenging for search methods. To address the challenge, we develop efficient rejection protocols to quickly filter out candidate layers that do not work well. We also use multi-objective evolution to optimize each layer's performance across many architectures to prevent overfitting. Our method leads to the discovery of EvoNorms, a set of new normalization-activation layers with novel, and sometimes surprising structures that go beyond existing design patterns. For example, some EvoNorms do not assume that normalization and activation functions must be applied sequentially, nor need to center the feature maps, nor require explicit activation functions. Our experiments show that EvoNorms work well on image classification models including ResNets, MobileNets and EfficientNets but also transfer well to Mask R-CNN with FPN/SpineNet for instance segmentation and to BigGAN for image synthesis, outperforming BatchNorm and GroupNorm based layers in many cases.

Transfer learning leverages feature representations of deep neural networks (DNNs) pretrained on source tasks with rich data to empower effective finetuning on downstream tasks. However, the pretrained models are often prohibitively large for delivering generalizable representations, which limits their deployment on edge devices with constrained resources. To close this gap, we propose a new transfer learning pipeline, which leverages our finding that robust tickets can transfer better, i.e., subnetworks drawn with properly induced adversarial robustness can win better transferability over vanilla lottery ticket subnetworks. Extensive experiments and ablation studies validate that our proposed transfer learning pipeline can achieve enhanced accuracy-sparsity trade-offs across both diverse downstream tasks and sparsity patterns, further enriching the lottery ticket hypothesis.

We present the OMG-CMDP! algorithm for regret minimization in adversarial Contextual MDPs. The algorithm operates under the minimal assumptions of realizable function class and access to online least squares and log loss regression oracles. Our algorithm is efficient (assuming efficient online regression oracles), simple and robust to approximation errors. It enjoys an O(H^{2.5} T|S||A| ( mathcal{R(O) + H log(delta^{-1}) )}) regret guarantee, with T being the number of episodes, S the state space, A the action space, H the horizon and R(O) = R(O_{sq}^F) + R(O_{log}^P) is the sum of the regression oracles' regret, used to approximate the context-dependent rewards and dynamics, respectively. To the best of our knowledge, our algorithm is the first efficient rate optimal regret minimization algorithm for adversarial CMDPs that operates under the minimal standard assumption of online function approximation.

Federated learning (FL) is a trending training paradigm to utilize decentralized training data. FL allows clients to update model parameters locally for several epochs, then share them to a global model for aggregation. This training paradigm with multi-local step updating before aggregation exposes unique vulnerabilities to adversarial attacks. Adversarial training is a popular and effective method to improve the robustness of networks against adversaries. In this work, we formulate a general form of federated adversarial learning (FAL) that is adapted from adversarial learning in the centralized setting. On the client side of FL training, FAL has an inner loop to generate adversarial samples for adversarial training and an outer loop to update local model parameters. On the server side, FAL aggregates local model updates and broadcast the aggregated model. We design a global robust training loss and formulate FAL training as a min-max optimization problem. Unlike the convergence analysis in classical centralized training that relies on the gradient direction, it is significantly harder to analyze the convergence in FAL for three reasons: 1) the complexity of min-max optimization, 2) model not updating in the gradient direction due to the multi-local updates on the client-side before aggregation and 3) inter-client heterogeneity. We address these challenges by using appropriate gradient approximation and coupling techniques and present the convergence analysis in the over-parameterized regime. Our main result theoretically shows that the minimum loss under our algorithm can converge to epsilon small with chosen learning rate and communication rounds. It is noteworthy that our analysis is feasible for non-IID clients.

Most recent test-time adaptation methods focus on only classification tasks, use specialized network architectures, destroy model calibration or rely on lightweight information from the source domain. To tackle these issues, this paper proposes a novel Test-time Self-Learning method with automatic Adversarial augmentation dubbed TeSLA for adapting a pre-trained source model to the unlabeled streaming test data. In contrast to conventional self-learning methods based on cross-entropy, we introduce a new test-time loss function through an implicitly tight connection with the mutual information and online knowledge distillation. Furthermore, we propose a learnable efficient adversarial augmentation module that further enhances online knowledge distillation by simulating high entropy augmented images. Our method achieves state-of-the-art classification and segmentation results on several benchmarks and types of domain shifts, particularly on challenging measurement shifts of medical images. TeSLA also benefits from several desirable properties compared to competing methods in terms of calibration, uncertainty metrics, insensitivity to model architectures, and source training strategies, all supported by extensive ablations. Our code and models are available on GitHub.

In recent years, neural networks have become the default choice for image classification and many other learning tasks, even though they are vulnerable to so-called adversarial attacks. To increase their robustness against these attacks, there have emerged numerous detection mechanisms that aim to automatically determine if an input is adversarial. However, state-of-the-art detection mechanisms either rely on being tuned for each type of attack, or they do not generalize across different attack types. To alleviate these issues, we propose a novel technique for adversarial-image detection, RAID, that trains a secondary classifier to identify differences in neuron activation values between benign and adversarial inputs. Our technique is both more reliable and more effective than the state of the art when evaluated against six popular attacks. Moreover, a straightforward extension of RAID increases its robustness against detection-aware adversaries without affecting its effectiveness.

The goal of lifelong learning is to continuously learn from non-stationary distributions, where the non-stationarity is typically imposed by a sequence of distinct tasks. Prior works have mostly considered idealistic settings, where the identity of tasks is known at least at training. In this paper we focus on a fundamentally harder, so-called task-agnostic setting where the task identities are not known and the learning machine needs to infer them from the observations. Our algorithm, which we call TAME (Task-Agnostic continual learning using Multiple Experts), automatically detects the shift in data distributions and switches between task expert networks in an online manner. At training, the strategy for switching between tasks hinges on an extremely simple observation that for each new coming task there occurs a statistically-significant deviation in the value of the loss function that marks the onset of this new task. At inference, the switching between experts is governed by the selector network that forwards the test sample to its relevant expert network. The selector network is trained on a small subset of data drawn uniformly at random. We control the growth of the task expert networks as well as selector network by employing online pruning. Our experimental results show the efficacy of our approach on benchmark continual learning data sets, outperforming the previous task-agnostic methods and even the techniques that admit task identities at both training and testing, while at the same time using a comparable model size.

Recent research finds CNN models for image classification demonstrate overlapped adversarial vulnerabilities: adversarial attacks can mislead CNN models with small perturbations, which can effectively transfer between different models trained on the same dataset. Adversarial training, as a general robustness improvement technique, eliminates the vulnerability in a single model by forcing it to learn robust features. The process is hard, often requires models with large capacity, and suffers from significant loss on clean data accuracy. Alternatively, ensemble methods are proposed to induce sub-models with diverse outputs against a transfer adversarial example, making the ensemble robust against transfer attacks even if each sub-model is individually non-robust. Only small clean accuracy drop is observed in the process. However, previous ensemble training methods are not efficacious in inducing such diversity and thus ineffective on reaching robust ensemble. We propose DVERGE, which isolates the adversarial vulnerability in each sub-model by distilling non-robust features, and diversifies the adversarial vulnerability to induce diverse outputs against a transfer attack. The novel diversity metric and training procedure enables DVERGE to achieve higher robustness against transfer attacks comparing to previous ensemble methods, and enables the improved robustness when more sub-models are added to the ensemble. The code of this work is available at https://github.com/zjysteven/DVERGE

Generalizing to unseen image domains is a challenging problem primarily due to the lack of diverse training data, inaccessible target data, and the large domain shift that may exist in many real-world settings. As such data augmentation is a critical component of domain generalization methods that seek to address this problem. We present Adversarial Bayesian Augmentation (ABA), a novel algorithm that learns to generate image augmentations in the challenging single-source domain generalization setting. ABA draws on the strengths of adversarial learning and Bayesian neural networks to guide the generation of diverse data augmentations -- these synthesized image domains aid the classifier in generalizing to unseen domains. We demonstrate the strength of ABA on several types of domain shift including style shift, subpopulation shift, and shift in the medical imaging setting. ABA outperforms all previous state-of-the-art methods, including pre-specified augmentations, pixel-based and convolutional-based augmentations.

Catastrophic overfitting (CO) in single-step adversarial training (AT) results in abrupt drops in the adversarial test accuracy (even down to 0%). For models trained with multi-step AT, it has been observed that the loss function behaves locally linearly with respect to the input, this is however lost in single-step AT. To address CO in single-step AT, several methods have been proposed to enforce local linearity of the loss via regularization. However, these regularization terms considerably slow down training due to Double Backpropagation. Instead, in this work, we introduce a regularization term, called ELLE, to mitigate CO effectively and efficiently in classical AT evaluations, as well as some more difficult regimes, e.g., large adversarial perturbations and long training schedules. Our regularization term can be theoretically linked to curvature of the loss function and is computationally cheaper than previous methods by avoiding Double Backpropagation. Our thorough experimental validation demonstrates that our work does not suffer from CO, even in challenging settings where previous works suffer from it. We also notice that adapting our regularization parameter during training (ELLE-A) greatly improves the performance, specially in large epsilon setups. Our implementation is available in https://github.com/LIONS-EPFL/ELLE .

We study the cost of overfitting in noisy kernel ridge regression (KRR), which we define as the ratio between the test error of the interpolating ridgeless model and the test error of the optimally-tuned model. We take an "agnostic" view in the following sense: we consider the cost as a function of sample size for any target function, even if the sample size is not large enough for consistency or the target is outside the RKHS. We analyze the cost of overfitting under a Gaussian universality ansatz using recently derived (non-rigorous) risk estimates in terms of the task eigenstructure. Our analysis provides a more refined characterization of benign, tempered and catastrophic overfitting (cf. Mallinar et al. 2022).

The disparity in accuracy between classes in standard training is amplified during adversarial training, a phenomenon termed the robust fairness problem. Existing methodologies aimed to enhance robust fairness by sacrificing the model's performance on easier classes in order to improve its performance on harder ones. However, we observe that under adversarial attacks, the majority of the model's predictions for samples from the worst class are biased towards classes similar to the worst class, rather than towards the easy classes. Through theoretical and empirical analysis, we demonstrate that robust fairness deteriorates as the distance between classes decreases. Motivated by these insights, we introduce the Distance-Aware Fair Adversarial training (DAFA) methodology, which addresses robust fairness by taking into account the similarities between classes. Specifically, our method assigns distinct loss weights and adversarial margins to each class and adjusts them to encourage a trade-off in robustness among similar classes. Experimental results across various datasets demonstrate that our method not only maintains average robust accuracy but also significantly improves the worst robust accuracy, indicating a marked improvement in robust fairness compared to existing methods.

Normal-form games (NFGs) are the fundamental model of strategic interaction. We study their representation using neural networks. We describe the inherent equivariance of NFGs -- any permutation of strategies describes an equivalent game -- as well as the challenges this poses for representation learning. We then propose the NfgTransformer architecture that leverages this equivariance, leading to state-of-the-art performance in a range of game-theoretic tasks including equilibrium-solving, deviation gain estimation and ranking, with a common approach to NFG representation. We show that the resulting model is interpretable and versatile, paving the way towards deep learning systems capable of game-theoretic reasoning when interacting with humans and with each other.

In this work, we propose a framework to learn feedback control policies with guarantees on closed-loop generalization and adversarial robustness. These policies are learned directly from expert demonstrations, contained in a dataset of state-control input pairs, without any prior knowledge of the task and system model. We use a Lipschitz-constrained loss minimization scheme to learn feedback policies with certified closed-loop robustness, wherein the Lipschitz constraint serves as a mechanism to tune the generalization performance and robustness to adversarial disturbances. Our analysis exploits the Lipschitz property to obtain closed-loop guarantees on generalization and robustness of the learned policies. In particular, we derive a finite sample bound on the policy learning error and establish robust closed-loop stability under the learned control policy. We also derive bounds on the closed-loop regret with respect to the expert policy and the deterioration of closed-loop performance under bounded (adversarial) disturbances to the state measurements. Numerical results validate our analysis and demonstrate the effectiveness of our robust feedback policy learning framework. Finally, our results suggest the existence of a potential tradeoff between nominal closed-loop performance and adversarial robustness, and that improvements in nominal closed-loop performance can only be made at the expense of robustness to adversarial perturbations.

Conventional wisdom suggests that neural network predictions tend to be unpredictable and overconfident when faced with out-of-distribution (OOD) inputs. Our work reassesses this assumption for neural networks with high-dimensional inputs. Rather than extrapolating in arbitrary ways, we observe that neural network predictions often tend towards a constant value as input data becomes increasingly OOD. Moreover, we find that this value often closely approximates the optimal constant solution (OCS), i.e., the prediction that minimizes the average loss over the training data without observing the input. We present results showing this phenomenon across 8 datasets with different distributional shifts (including CIFAR10-C and ImageNet-R, S), different loss functions (cross entropy, MSE, and Gaussian NLL), and different architectures (CNNs and transformers). Furthermore, we present an explanation for this behavior, which we first validate empirically and then study theoretically in a simplified setting involving deep homogeneous networks with ReLU activations. Finally, we show how one can leverage our insights in practice to enable risk-sensitive decision-making in the presence of OOD inputs.

Training deep neural networks requires intricate initialization and careful selection of learning rates. The emergence of stochastic gradient optimization methods that use adaptive learning rates based on squared past gradients, e.g., AdaGrad, AdaDelta, and Adam, eases the job slightly. However, such methods have also been proven problematic in recent studies with their own pitfalls including non-convergence issues and so on. Alternative variants have been proposed for enhancement, such as AMSGrad, AdaShift and AdaBound. In this work, we identify a new problem of adaptive learning rate methods that exhibits at the beginning of learning where Adam produces extremely large learning rates that inhibit the start of learning. We propose the Adaptive and Momental Bound (AdaMod) method to restrict the adaptive learning rates with adaptive and momental upper bounds. The dynamic learning rate bounds are based on the exponential moving averages of the adaptive learning rates themselves, which smooth out unexpected large learning rates and stabilize the training of deep neural networks. Our experiments verify that AdaMod eliminates the extremely large learning rates throughout the training and brings significant improvements especially on complex networks such as DenseNet and Transformer, compared to Adam. Our implementation is available at: https://github.com/lancopku/AdaMod

We introduce distributional dynamic programming (DP) methods for optimizing statistical functionals of the return distribution, with standard reinforcement learning as a special case. Previous distributional DP methods could optimize the same class of expected utilities as classic DP. To go beyond expected utilities, we combine distributional DP with stock augmentation, a technique previously introduced for classic DP in the context of risk-sensitive RL, where the MDP state is augmented with a statistic of the rewards obtained so far (since the first time step). We find that a number of recently studied problems can be formulated as stock-augmented return distribution optimization, and we show that we can use distributional DP to solve them. We analyze distributional value and policy iteration, with bounds and a study of what objectives these distributional DP methods can or cannot optimize. We describe a number of applications outlining how to use distributional DP to solve different stock-augmented return distribution optimization problems, for example maximizing conditional value-at-risk, and homeostatic regulation. To highlight the practical potential of stock-augmented return distribution optimization and distributional DP, we combine the core ideas of distributional value iteration with the deep RL agent DQN, and empirically evaluate it for solving instances of the applications discussed.

We show that the basic classification framework alone can be used to tackle some of the most challenging tasks in image synthesis. In contrast to other state-of-the-art approaches, the toolkit we develop is rather minimal: it uses a single, off-the-shelf classifier for all these tasks. The crux of our approach is that we train this classifier to be adversarially robust. It turns out that adversarial robustness is precisely what we need to directly manipulate salient features of the input. Overall, our findings demonstrate the utility of robustness in the broader machine learning context. Code and models for our experiments can be found at https://git.io/robust-apps.

Architecture optimization, which is a technique for finding an efficient neural network that meets certain requirements, generally reduces to a set of multiple-choice selection problems among alternative sub-structures or parameters. The discrete nature of the selection problem, however, makes this optimization difficult. To tackle this problem we introduce a novel concept of a trainable gate function. The trainable gate function, which confers a differentiable property to discretevalued variables, allows us to directly optimize loss functions that include non-differentiable discrete values such as 0-1 selection. The proposed trainable gate can be applied to pruning. Pruning can be carried out simply by appending the proposed trainable gate functions to each intermediate output tensor followed by fine-tuning the overall model, using any gradient-based training methods. So the proposed method can jointly optimize the selection of the pruned channels while fine-tuning the weights of the pruned model at the same time. Our experimental results demonstrate that the proposed method efficiently optimizes arbitrary neural networks in various tasks such as image classification, style transfer, optical flow estimation, and neural machine translation.

Domain adaptation (DA) attempts to transfer the knowledge from a labeled source domain to an unlabeled target domain that follows different distribution from the source. To achieve this, DA methods include a source classification objective to extract the source knowledge and a domain alignment objective to diminish the domain shift, ensuring knowledge transfer. Typically, former DA methods adopt some weight hyper-parameters to linearly combine the training objectives to form an overall objective. However, the gradient directions of these objectives may conflict with each other due to domain shift. Under such circumstances, the linear optimization scheme might decrease the overall objective value at the expense of damaging one of the training objectives, leading to restricted solutions. In this paper, we rethink the optimization scheme for DA from a gradient-based perspective. We propose a Pareto Domain Adaptation (ParetoDA) approach to control the overall optimization direction, aiming to cooperatively optimize all training objectives. Specifically, to reach a desirable solution on the target domain, we design a surrogate loss mimicking target classification. To improve target-prediction accuracy to support the mimicking, we propose a target-prediction refining mechanism which exploits domain labels via Bayes' theorem. On the other hand, since prior knowledge of weighting schemes for objectives is often unavailable to guide optimization to approach the optimal solution on the target domain, we propose a dynamic preference mechanism to dynamically guide our cooperative optimization by the gradient of the surrogate loss on a held-out unlabeled target dataset. Extensive experiments on image classification and semantic segmentation benchmarks demonstrate the effectiveness of ParetoDA

An abundance of recent impossibility results establish that regret minimization in Markov games with adversarial opponents is both statistically and computationally intractable. Nevertheless, none of these results preclude the possibility of regret minimization under the assumption that all parties adopt the same learning procedure. In this work, we present the first (to our knowledge) algorithm for learning in general-sum Markov games that provides sublinear regret guarantees when executed by all agents. The bounds we obtain are for swap regret, and thus, along the way, imply convergence to a correlated equilibrium. Our algorithm is decentralized, computationally efficient, and does not require any communication between agents. Our key observation is that online learning via policy optimization in Markov games essentially reduces to a form of weighted regret minimization, with unknown weights determined by the path length of the agents' policy sequence. Consequently, controlling the path length leads to weighted regret objectives for which sufficiently adaptive algorithms provide sublinear regret guarantees.

3D Gaussian splatting (3DGS), known for its groundbreaking performance and efficiency, has become a dominant 3D representation and brought progress to many 3D vision tasks. However, in this work, we reveal a significant security vulnerability that has been largely overlooked in 3DGS: the computation cost of training 3DGS could be maliciously tampered by poisoning the input data. By developing an attack named Poison-splat, we reveal a novel attack surface where the adversary can poison the input images to drastically increase the computation memory and time needed for 3DGS training, pushing the algorithm towards its worst computation complexity. In extreme cases, the attack can even consume all allocable memory, leading to a Denial-of-Service (DoS) that disrupts servers, resulting in practical damages to real-world 3DGS service vendors. Such a computation cost attack is achieved by addressing a bi-level optimization problem through three tailored strategies: attack objective approximation, proxy model rendering, and optional constrained optimization. These strategies not only ensure the effectiveness of our attack but also make it difficult to defend with simple defensive measures. We hope the revelation of this novel attack surface can spark attention to this crucial yet overlooked vulnerability of 3DGS systems. Our code is available at https://github.com/jiahaolu97/poison-splat .

Mammalian brains handle complex reasoning tasks in a gestalt manner by integrating information from regions of the brain that are specialised to individual sensory modalities. This allows for improved robustness and better generalisation ability. In contrast, deep neural networks are usually designed to process one particular information stream and susceptible to various types of adversarial perturbations. While many methods exist for detecting and defending against adversarial attacks, they do not generalise across a range of attacks and negatively affect performance on clean, unperturbed data. We developed a fusion model using a combination of background and foreground features extracted in parallel from Places-CNN and Imagenet-CNN. We tested the benefits of the fusion approach on preserving adversarial robustness for human perceivable (e.g., Gaussian blur) and network perceivable (e.g., gradient-based) attacks for CIFAR-10 and MS COCO data sets. For gradient based attacks, our results show that fusion allows for significant improvements in classification without decreasing performance on unperturbed data and without need to perform adversarial retraining. Our fused model revealed improvements for Gaussian blur type perturbations as well. The increase in performance from fusion approach depended on the variability of the image contexts; larger increases were seen for classes of images with larger differences in their contexts. We also demonstrate the effect of regularization to bias the classifier decision in the presence of a known adversary. We propose that this biologically inspired approach to integrate information across multiple modalities provides a new way to improve adversarial robustness that can be complementary to current state of the art approaches.

We study a K-armed bandit with delayed feedback and intermediate observations. We consider a model where intermediate observations have a form of a finite state, which is observed immediately after taking an action, whereas the loss is observed after an adversarially chosen delay. We show that the regime of the mapping of states to losses determines the complexity of the problem, irrespective of whether the mapping of actions to states is stochastic or adversarial. If the mapping of states to losses is adversarial, then the regret rate is of order (K+d)T (within log factors), where T is the time horizon and d is a fixed delay. This matches the regret rate of a K-armed bandit with delayed feedback and without intermediate observations, implying that intermediate observations are not helpful. However, if the mapping of states to losses is stochastic, we show that the regret grows at a rate of big(K+min{|mathcal{S|,d}big)T} (within log factors), implying that if the number |S| of states is smaller than the delay, then intermediate observations help. We also provide refined high-probability regret upper bounds for non-uniform delays, together with experimental validation of our algorithms.

The study of adversarial vulnerabilities of deep neural networks (DNNs) has progressed rapidly. Existing attacks require either internal access (to the architecture, parameters, or training set of the victim model) or external access (to query the model). However, both the access may be infeasible or expensive in many scenarios. We investigate no-box adversarial examples, where the attacker can neither access the model information or the training set nor query the model. Instead, the attacker can only gather a small number of examples from the same problem domain as that of the victim model. Such a stronger threat model greatly expands the applicability of adversarial attacks. We propose three mechanisms for training with a very small dataset (on the order of tens of examples) and find that prototypical reconstruction is the most effective. Our experiments show that adversarial examples crafted on prototypical auto-encoding models transfer well to a variety of image classification and face verification models. On a commercial celebrity recognition system held by clarifai.com, our approach significantly diminishes the average prediction accuracy of the system to only 15.40%, which is on par with the attack that transfers adversarial examples from a pre-trained Arcface model.

Recent work has shown that it is possible to train deep neural networks that are provably robust to norm-bounded adversarial perturbations. Most of these methods are based on minimizing an upper bound on the worst-case loss over all possible adversarial perturbations. While these techniques show promise, they often result in difficult optimization procedures that remain hard to scale to larger networks. Through a comprehensive analysis, we show how a simple bounding technique, interval bound propagation (IBP), can be exploited to train large provably robust neural networks that beat the state-of-the-art in verified accuracy. While the upper bound computed by IBP can be quite weak for general networks, we demonstrate that an appropriate loss and clever hyper-parameter schedule allow the network to adapt such that the IBP bound is tight. This results in a fast and stable learning algorithm that outperforms more sophisticated methods and achieves state-of-the-art results on MNIST, CIFAR-10 and SVHN. It also allows us to train the largest model to be verified beyond vacuous bounds on a downscaled version of ImageNet.

Despite unconditional feature inversion being the foundation of many image synthesis applications, training an inverter demands a high computational budget, large decoding capacity and imposing conditions such as autoregressive priors. To address these limitations, we propose the use of adversarially robust representations as a perceptual primitive for feature inversion. We train an adversarially robust encoder to extract disentangled and perceptually-aligned image representations, making them easily invertible. By training a simple generator with the mirror architecture of the encoder, we achieve superior reconstruction quality and generalization over standard models. Based on this, we propose an adversarially robust autoencoder and demonstrate its improved performance on style transfer, image denoising and anomaly detection tasks. Compared to recent ImageNet feature inversion methods, our model attains improved performance with significantly less complexity.

We propose that the grokking phenomenon, where the train loss of a neural network decreases much earlier than its test loss, can arise due to a neural network transitioning from lazy training dynamics to a rich, feature learning regime. To illustrate this mechanism, we study the simple setting of vanilla gradient descent on a polynomial regression problem with a two layer neural network which exhibits grokking without regularization in a way that cannot be explained by existing theories. We identify sufficient statistics for the test loss of such a network, and tracking these over training reveals that grokking arises in this setting when the network first attempts to fit a kernel regression solution with its initial features, followed by late-time feature learning where a generalizing solution is identified after train loss is already low. We provide an asymptotic theoretical description of the grokking dynamics in this model using dynamical mean field theory (DMFT) for high dimensional data. We find that the key determinants of grokking are the rate of feature learning -- which can be controlled precisely by parameters that scale the network output -- and the alignment of the initial features with the target function y(x). We argue this delayed generalization arises when (1) the top eigenvectors of the initial neural tangent kernel and the task labels y(x) are misaligned, but (2) the dataset size is large enough so that it is possible for the network to generalize eventually, but not so large that train loss perfectly tracks test loss at all epochs, and (3) the network begins training in the lazy regime so does not learn features immediately. We conclude with evidence that this transition from lazy (linear model) to rich training (feature learning) can control grokking in more general settings, like on MNIST, one-layer Transformers, and student-teacher networks.

The vast majority of Reinforcement Learning methods is largely impacted by the computation effort and data requirements needed to obtain effective estimates of action-value functions, which in turn determine the quality of the overall performance and the sample-efficiency of the learning procedure. Typically, action-value functions are estimated through an iterative scheme that alternates the application of an empirical approximation of the Bellman operator and a subsequent projection step onto a considered function space. It has been observed that this scheme can be potentially generalized to carry out multiple iterations of the Bellman operator at once, benefiting the underlying learning algorithm. However, till now, it has been challenging to effectively implement this idea, especially in high-dimensional problems. In this paper, we introduce iterated Q-Network (i-QN), a novel principled approach that enables multiple consecutive Bellman updates by learning a tailored sequence of action-value functions where each serves as the target for the next. We show that i-QN is theoretically grounded and that it can be seamlessly used in value-based and actor-critic methods. We empirically demonstrate the advantages of i-QN in Atari 2600 games and MuJoCo continuous control problems.

Deep neural networks (DNNs) offer significant promise for improving breast cancer diagnosis in medical imaging. However, these models are highly susceptible to adversarial attacks--small, imperceptible changes that can mislead classifiers--raising critical concerns about their reliability and security. Traditional attacks rely on fixed-norm perturbations, misaligning with human perception. In contrast, diffusion-based attacks require pre-trained models, demanding substantial data when these models are unavailable, limiting practical use in data-scarce scenarios. In medical imaging, however, this is often unfeasible due to the limited availability of datasets. Building on recent advancements in learnable prompts, we propose Prompt2Perturb (P2P), a novel language-guided attack method capable of generating meaningful attack examples driven by text instructions. During the prompt learning phase, our approach leverages learnable prompts within the text encoder to create subtle, yet impactful, perturbations that remain imperceptible while guiding the model towards targeted outcomes. In contrast to current prompt learning-based approaches, our P2P stands out by directly updating text embeddings, avoiding the need for retraining diffusion models. Further, we leverage the finding that optimizing only the early reverse diffusion steps boosts efficiency while ensuring that the generated adversarial examples incorporate subtle noise, thus preserving ultrasound image quality without introducing noticeable artifacts. We show that our method outperforms state-of-the-art attack techniques across three breast ultrasound datasets in FID and LPIPS. Moreover, the generated images are both more natural in appearance and more effective compared to existing adversarial attacks. Our code will be publicly available https://github.com/yasamin-med/P2P.