Non-Asymptotic Bounds for Adversarial Excess Risk under Misspecified Models
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Abstract (arXiv)
We propose a general approach to evaluating the performance of robust estimators based on adversarial losses under misspecified models. We first show that adversarial risk is equivalent to the risk induced by a distributional adversarial attack under certain smoothness conditions. This ensures that the adversarial training procedure is well-defined. To evaluate the generalization performance of the adversarial estimator, we study the adversarial excess risk. Our proposed analysis method includes investigations on both generalization error and approximation error. We then establish non-asymptotic upper bounds for the adversarial excess risk associated with Lipschitz loss functions. In addition, we apply our general results to adversarial training for classification and regression problems. For the quadratic loss in nonparametric regression, we show that the adversarial excess risk bound can be improved over those for a general loss.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 42 of its 59 references that are in the map. First posted on arXiv 2 Sep 2023.
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42 of 59 references.
References · 42
- 2014Explaining and Harnessing Adversarial Examplescited by 7,364
- 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,415
- 2013Intriguing properties of neural networkscited by 5,155
- 2016Towards Evaluating the Robustness of Neural Networkscited by 2,998
- 2019Theoretically Principled Trade-off between Robustness and Accuracycited by 1,517
- 2019Certified Adversarial Robustness via Randomized Smoothingcited by 1,340
- 2015DeepFool: a simple and accurate method to fool deep neural networkscited by 1,318
- 2018Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examplescited by 1,268
- 2018Robustness May Be at Odds with Accuracycited by 880
- 2015The Limitations of Deep Learning in Adversarial Settingscited by 790
- 2015Distillation as a Defense to Adversarial Perturbations against Deep Neural Networkscited by 678
- 2017One pixel attack for fooling deep neural networkscited by 582
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- 2017Decision-Based Adversarial Attacks: Reliable Attacks Against Black-Box Machine Learning Modelscited by 462
- 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 433
- 2018Adversarially Robust Generalization Requires More Datacited by 318
- 2017Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networkscited by 311
- 2018Certified Defenses against Adversarial Examplescited by 306
- 2017Parseval Networks: Improving Robustness to Adversarial Examplescited by 293
- 2018Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networkscited by 195
- 2018Optimal approximation of continuous functions by very deep ReLU networkscited by 166
- 2020Deep Network Approximation for Smooth Functionscited by 164
- 2021A Universal Law of Robustness via Isoperimetrycited by 151
- 2018Rademacher Complexity for Adversarially Robust Generalizationcited by 132
- 2019Adversarial Training Can Hurt Generalizationcited by 132
- 2020Precise Tradeoffs in Adversarial Training for Linear Regressioncited by 77
- 2020Precise Statistical Analysis of Classification Accuracies for Adversarial Trainingcited by 50
- 2020Adversarial Learning Guarantees for Linear Hypotheses and Neural Networkscited by 47
- 2021Calibration and Consistency of Adversarial Surrogate Lossescited by 47
- 2020Provable tradeoffs in adversarially robust classificationcited by 40
- 2019Adversarial Risk via Optimal Transport and Optimal Couplingscited by 36
- 2020Calibrated Surrogate Losses for Adversarially Robust Classificationcited by 36
- 2018Theoretical Analysis of Adversarial Learning: A Minimax Approachcited by 31
- 2020Sharp Statistical Guarantees for Adversarially Robust Gaussian Classificationcited by 28
- 2022The Many Faces of Adversarial Riskcited by 28
- 2021A Finer Calibration Analysis for Adversarial Robustnesscited by 26
- 2021On the Existence of the Adversarial Bayes Classifier (Extended Version)cited by 25
- 2021Wasserstein Generative Learning of Conditional Distributioncited by 24
- 2020Adversarially Robust Estimate and Risk Analysis in Linear Regressioncited by 22
- 2022Approximation bounds for norm constrained neural networks with applications to regression and GANscited by 22
- 2021The Geometry of Adversarial Training in Binary Classificationcited by 20
- 2022Existence and Minimax Theorems for Adversarial Surrogate Risks in Binary Classificationcited by 15
- 2022Towards Consistency in Adversarial Classificationcited by 12
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