mlsanityData to 7 Oct 2026

The Many Faces of Adversarial Risk

arXiv 2201.08956 ↗First posted 22 Jan 2022stat.ML cs.IT cs.LGcited by 28

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Abstract (arXiv)

Adversarial risk quantifies the performance of classifiers on adversarially perturbed data. Numerous definitions of adversarial risk -- not all mathematically rigorous and differing subtly in the details -- have appeared in the literature. In this paper, we revisit these definitions, make them rigorous, and critically examine their similarities and differences. Our technical tools derive from optimal transport, robust statistics, functional analysis, and game theory. Our contributions include the following: generalizing Strassen's theorem to the unbalanced optimal transport setting with applications to adversarial classification with unequal priors; showing an equivalence between adversarial robustness and robust hypothesis testing with ∞-Wasserstein uncertainty sets; proving the existence of a pure Nash equilibrium in the two-player game between the adversary and the algorithm; and characterizing adversarial risk by the minimum Bayes error between a pair of distributions belonging to the ∞-Wasserstein uncertainty sets. Our results generalize and deepen recently discovered connections between optimal transport and adversarial robustness and reveal new connections to Choquet capacities and game theory.

Key facts. Cited by 28 papers in the map (data through 7 Oct 2026). Builds on 32 of its 63 references that are in the map. First posted on arXiv 22 Jan 2022.

Builds on

32 of 63 references.

References · 32

  1. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
  2. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
  3. 2013Intriguing properties of neural networkscited by 5,114
  4. 2016Towards Evaluating the Robustness of Neural Networkscited by 2,976
  5. 2019Certified Adversarial Robustness via Randomized Smoothingcited by 1,324
  6. 2015Distillation as a Defense to Adversarial Perturbations against Deep Neural Networkscited by 675
  7. 2019A Survey of Deep Learning Techniques for Autonomous Drivingcited by 401
  8. 2017Certifying Some Distributional Robustness with Principled Adversarial Trainingcited by 333
  9. 2018Adversarial Risk and the Dangers of Evaluating Against Weak Attackscited by 221
  10. 2019Understanding Adversarial Attacks on Deep Learning Based Medical Image Analysis Systemscited by 151
  11. 2019Lower Bounds on Adversarial Robustness from Optimal Transportcited by 52
  12. 2018The Curse of Concentration in Robust Learning: Evasion and Poisoning Attacks from Concentration of Measurecited by 44
20 more
  1. 2020Randomization matters. How to defend against strong adversarial attackscited by 37
  2. 2019Adversarial Risk via Optimal Transport and Optimal Couplingscited by 36
  3. 2017The Robust Manifold Defense: Adversarial Training using Generative Modelscited by 35
  4. 2020Adversarial Example Gamescited by 34
  5. 2018Adversarial Risk and Robustness: General Definitions and Implications for the Uniform Distributioncited by 32
  6. 2018Theoretical Analysis of Adversarial Learning: A Minimax Approachcited by 31
  7. 2020Learn2Perturb: an End-to-end Feature Perturbation Learning to Improve Adversarial Robustnesscited by 27
  8. 2019On the Hardness of Robust Classificationcited by 23
  9. 2020On Linear Optimization over Wasserstein Ballscited by 23
  10. 2021Mixed Nash Equilibria in the Adversarial Examples Gamecited by 22
  11. 2020Adversarial Classification: Necessary conditions and geometric flowscited by 19
  12. 2018Learning to Defend by Learning to Attackcited by 17
  13. 2020When are Non-Parametric Methods Robust?cited by 15
  14. 2016Randomized Prediction Games for Adversarial Machine Learningcited by 11
  15. 2018Revisiting Adversarial Riskcited by 9
  16. 2018Law and Adversarial Machine Learningcited by 5
  17. 2017Asymptotic Coupling and Its Applications in Information Theorycited by 4
  18. 2019Robustifying deep networks for image segmentationcited by 2
  19. 2020Classifier-independent Lower-Bounds for Adversarial Robustnesscited by 1
  20. 2021Robustness-via-Synthesis: Robust Training with Generative Adversarial Perturbationscited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 6; 2023: 10; 2024: 6; 2025: 4; 2026: 2.

28 papers.

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  1. 2022The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classificationcited by 21
  2. 2022Existence and Minimax Theorems for Adversarial Surrogate Risks in Binary Classificationcited by 15
  3. 2022Towards Consistency in Adversarial Classificationcited by 12
  4. 2022Gamma-convergence of a nonlocal perimeter arising in adversarial machine learningcited by 10
  5. 2023It Is All About Data: A Survey on the Effects of Data on Adversarial Robustnesscited by 9
  6. 2023On the existence of solutions to adversarial training in multiclass classificationcited by 9
  7. 2023Characterizing the Optimal 0-1 Loss for Multi-class Classification with a Test-time Attackercited by 6
  8. 2023The Adversarial Consistency of Surrogate Risks for Binary Classificationcited by 6
  9. 2023On adversarial robustness and the use of Wasserstein ascent-descent dynamics to enforce itcited by 4
  10. 2023On the Role of Randomization in Adversarially Robust Classificationcited by 4
  11. 2024A mean curvature flow arising in adversarial trainingcited by 4
  12. 2025Adversarial Attacks against Neural Ranking Models via In-Context Learningcited by 4
16 more
  1. 2022The Consistency of Adversarial Training for Binary Classificationcited by 3
  2. 2023It begins with a boundary: A geometric view on probabilistically robust learningcited by 3
  3. 2024A Notion of Uniqueness for the Adversarial Bayes Classifiercited by 3
  4. 2023On the Hardness of Robustness Transfer: A Perspective from Rademacher Complexity over Symmetric Difference Hypothesis Spacecited by 2
  5. 2023Non-Asymptotic Bounds for Adversarial Excess Risk under Misspecified Modelscited by 2
  6. 2024Adversarial Consistency and the Uniqueness of the Adversarial Bayes Classifiercited by 2
  7. 2022When are Local Queries Useful for Robust Learning?cited by 1
  8. 2023Selecting Models based on the Risk of Damage Caused by Adversarial Attackscited by 1
  9. 2024Position: Towards Resilience Against Adversarial Examplescited by 1
  10. 2024Uniform Convergence of Adversarially Robust Classifierscited by 1
  11. 2025Adversarial Surrogate Risk Bounds for Binary Classificationcited by 1
  12. 2025Lower Bounds on Adversarial Robustness for Multiclass Classification with General Loss Functionscited by 1
  13. 2024Distributionally and Adversarially Robust Logistic Regression via Intersecting Wasserstein Ballscited by 0
  14. 2025Unveiling the Role of Randomization in Multiclass Adversarial Classification: Insights from Graph Theorycited by 0
  15. 2026Statistical Inference for Adversarial Training: Central Limit Theorems via Optimal Transportcited by 0
  16. 2026Distributionally robust linear regression through the lens of adversarial trainingcited by 0