As a research community, we are still lacking a systematic understanding of the progress on adversarial robustness, which often makes it hard to identify the most promising ideas in training robust models. A key challenge in benchmarking robustness is that its evaluation is often error-prone, leading to overestimation of the true robustness of models. While adaptive attacks designed for a particular defense are a potential solution, they have to be highly customized for particular models, which makes it difficult to compare different methods. Our goal is to instead establish a standardized benchmark of adversarial robustness, which as accurately as possible reflects the robustness of the considered models within a reasonable computational budget. To evaluate the robustness of models for our benchmark, we consider AutoAttack, an ensemble of white- and black-box attacks which was recently shown in a large-scale study to improve almost all robustness evaluations compared to the original publications. We also impose some restrictions on the admitted models to rule out defenses that only make gradient-based attacks ineffective without improving actual robustness. Our leaderboard, hosted at this https URL, contains evaluations of 90+ models and aims at reflecting the current state of the art on a set of well-defined tasks in $\ell_\infty$- and $\ell_2$-threat models and on common corruptions, with possible extensions in the future. Additionally, we open-source the library this https URL that provides unified access to 60+ robust models to facilitate their downstream applications. Finally, based on the collected models, we analyze the impact of robustness on the performance on distribution shifts, calibration, out-of-distribution detection, fairness, privacy leakage, smoothness, and transferability.

RobustBench: a standardized adversarial robustness benchmark.

We study online convex optimization with switching costs, a practically important but also extremely challenging problem due to the lack of complete offline information. By tapping into the power of machine learning (ML) based optimizers, ML-augmented online algorithms (also referred to as expert calibration in this paper) have been emerging as state of the art, with provable worst-case performance guarantees. Nonetheless, by using the standard practice of training an ML model as a standalone optimizer and plugging it into an ML-augmented algorithm, the average cost performance can be highly unsatisfactory. In order to address the "how to learn" challenge, we propose EC-L2O (expert-calibrated learning to optimize), which trains an ML-based optimizer by explicitly taking into account the downstream expert calibrator. To accomplish this, we propose a new differentiable expert calibrator that generalizes regularized online balanced descent and offers a provably better competitive ratio than pure ML predictions when the prediction error is large. For training, our loss function is a weighted sum of two different losses --- one minimizing the average ML prediction error for better robustness, and the other one minimizing the post-calibration average cost. We also provide theoretical analysis for EC-L2O, highlighting that expert calibration can be even beneficial for the average cost performance and that the high-percentile tail ratio of the cost achieved by EC-L2O to that of the offline optimal oracle (i.e., tail cost ratio) can be bounded. Finally, we test EC-L2O by running simulations for sustainable datacenter demand response. Our results demonstrate that EC-L2O can empirically achieve a lower average cost as well as a lower competitive ratio than the existing baseline algorithms.

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Expert-Calibrated Learning for Online Optimization with Switching Costs

Adversarial training (AT) is one of the most effective strategies for promoting model robustness, whereas even the state-of-the-art adversarially trained models struggle to exceed 60% robust test accuracy on CIFAR-10 without additional data, which is far from practical. A natural way to break this accuracy bottleneck is to introduce a rejection option, where confidence is a commonly used certainty proxy. However, the vanilla confidence can overestimate the model certainty if the input is wrongly classified. To this end, we propose to use true confidence (T-Con) (i.e., predicted probability of the true class) as a certainty oracle, and learn to predict T-Con by rectifying confidence. We prove that under mild conditions, a rectified confidence (R-Con) rejector and a confidence rejector can be coupled to distinguish any wrongly classified input from correctly classified ones, even under adaptive attacks. We also quantify that training R-Con to be aligned with T-Con could be an easier task than learning robust classifiers. In our experiments, we evaluate our rectified rejection (RR) module on CIFAR-10, CIFAR-10-C, and CIFAR-100 under several attacks, and demonstrate that the RR module is well compatible with different AT frameworks on improving robustness, with little extra computation.

Adversarial Training with Rectified Rejection

We investigate the problem of stabilizing an unknown networked linear system under communication constraints and adversarial disturbances. We propose the first provably stabilizing algorithm for the problem. The algorithm uses a distributed version of nested convex body chasing to maintain a consistent estimate of the network dynamics and applies system level synthesis to determine a distributed controller based on this estimated model. Our approach avoids the need for system identification and accommodates a broad class of communication delay while being fully distributed and scaling favorably with the number of subsystems.

/pdf/online-adversarial-stabilization-of-unknown-networked-vqwd20wv.pdf

Online Adversarial Stabilization of Unknown Networked Systems

Deep neural networks are known to be vulnerable to adversarially perturbed inputs. A commonly used defense is adversarial training, whose performance is influenced by model capacity. While previous works have studied the impact of varying model width and depth on robustness, the impact of increasing capacity by using learnable parametric activation functions (PAFs) has not been studied. We study how using learnable PAFs can improve robustness in conjunction with adversarial training. We first ask the question: how should we incorporate parameters into activation functions to improve robustness? To address this, we analyze the direct impact of activation shape on robustness through PAFs and observe that activation shapes with positive outputs on negative inputs and with high finite curvature can increase robustness. We combine these properties to create a new PAF, which we call Parametric Shifted Sigmoidal Linear Unit (PSSiLU). We then combine PAFs (including PReLU, PSoftplus and PSSiLU) with adversarial training and analyze robust performance. We find that PAFs optimize towards activation shape properties found to directly affect robustness. Additionally, we find that while introducing only 1-2 learnable parameters into the network, smooth PAFs can significantly increase robustness over ReLU. For instance, when trained on CIFAR-10 with additional synthetic data, PSSiLU improves robust accuracy by 4.54% over ReLU on ResNet-18 and 2.69% over ReLU on WRN-28-10 in the $\ell_{\infty}$ threat model while adding only 2 additional parameters into the network architecture. The PSSiLU WRN-28-10 model achieves 61.96% AutoAttack accuracy, improving over the state-of-the-art robust accuracy on RobustBench (Croce et al., 2020).

Parameterizing Activation Functions for Adversarial Robustness.

We consider the problem of convex function chasing with black-box advice, where an online decision-maker aims to minimize the total cost of making and switching between decisions in a normed vector space, aided by black-box advice such as the decisions of a machine-learned algorithm. The decision-maker seeks cost comparable to the advice when it performs well, known as consistency , while also ensuring worst-case robustness even when the advice is adversarial. We ﬁrst consider the common paradigm of algorithms that switch between the decisions of the advice and a competitive algorithm, showing that no algorithm in this class can improve upon 3-consistency while staying robust. We then propose two novel algorithms that bypass this limitation by exploiting the problem’s convexity. The ﬁrst, I NTERP , achieves ( √ 2 + (cid:15) ) -consistency and O ( C(cid:15) 2 ) -robustness for any (cid:15) > 0 , where C is the competitive ratio of an algorithm for convex function chasing or a subclass thereof. The second, B D I NTERP , achieves (1 + (cid:15) ) -consistency and O ( CD(cid:15) ) -robustness when the problem has bounded diameter D . Further, we show that B D I NTERP achieves near-optimal consistency-robustness trade-off for the special case where cost functions are α -polyhedral.

Chasing Convex Bodies and Functions with Black-Box Advice

We focus on the use of proxy distributions, i.e., approximations of the underlying distribution of the training dataset, in both understanding and improving the adversarial robustness in image classification. While additional training data helps in adversarial training, curating a very large number of real-world images is challenging. In contrast, proxy distributions enable us to sample a potentially unlimited number of images and improve adversarial robustness using these samples. We first ask the question: when does adversarial robustness benefit from incorporating additional samples from the proxy distribution in the training stage? We prove that the difference between the robustness of a classifier on the proxy and original training dataset distribution is upper bounded by the conditional Wasserstein distance between them. Our result confirms the intuition that samples from a proxy distribution that closely approximates training dataset distribution should be able to boost adversarial robustness. Motivated by this finding, we leverage samples from state-of-the-art generative models, which can closely approximate training data distribution, to improve robustness. In particular, we improve robust accuracy by up to 6.1% and 5.7% in $l_{\infty}$ and $l_2$ threat model, and certified robust accuracy by 6.7% over baselines not using proxy distributions on the CIFAR-10 dataset. Since we can sample an unlimited number of images from a proxy distribution, it also allows us to investigate the effect of an increasing number of training samples on adversarial robustness. Here we provide the first large scale empirical investigation of accuracy vs robustness trade-off and sample complexity of adversarial training by training deep neural networks on 2K to 10M images.

Improving Adversarial Robustness Using Proxy Distributions.

While additional training data improves the robustness of deep neural networks against adversarial examples, it presents the challenge of curating a large number of specific real-world samples. We circumvent this challenge by using additional data from proxy distributions learned by state-of-the-art generative models. We first seek to formally understand the transfer of robustness from classifiers trained on proxy distributions to the real data distribution. We prove that the difference between the robustness of a classifier on the two distributions is upper bounded by the conditional Wasserstein distance between them. Motivated by our result, we next ask how to empirically select an appropriate generative model? We find that existing distance metrics, such as FID, fail to correctly determine the robustness transfer from proxy distributions. We propose a robust discrimination approach, which measures the distinguishability of synthetic and real samples under adversarial perturbations. Our approach accurately predicts the robustness transfer from different proxy distributions. After choosing a proxy distribution, the next question is which samples are most beneficial? We successfully optimize this selection by estimating the importance of each sample in robustness transfer. Finally, using our selection criterion for proxy distribution and individual samples, we curate a set of ten million most beneficial synthetic samples for robust training on the CIFAR-10 dataset. Using this set we improve robust accuracy by up to 7.5% and 6.7% in $\ell_{\infty}$ and $\ell_2$ threat model, and certified robust accuracy by 7.6% in $\ell_2$ threat model over baselines not using proxy distributions on the CIFAR-10 dataset.

Tinashe Handina

Papers

Chasing Convex Bodies and Functions with Black-Box Advice

Improving Adversarial Robustness Using Proxy Distributions.

Robust Learning Meets Generative Models: Can Proxy Distributions Improve Adversarial Robustness?.