mlsanityData to 7 Oct 2026

Adversarial Risk via Optimal Transport and Optimal Couplings

arXiv 1912.02794 ↗First posted 5 Dec 2019cs.LG cs.IT math.ITcited by 36

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Abstract (arXiv)

Modern machine learning algorithms perform poorly on adversarially manipulated data. Adversarial risk quantifies the error of classifiers in adversarial settings; adversarial classifiers minimize adversarial risk. In this paper, we analyze adversarial risk and adversarial classifiers from an optimal transport perspective. We show that the optimal adversarial risk for binary classification with 0-1 loss is determined by an optimal transport cost between the probability distributions of the two classes. We develop optimal transport plans (probabilistic couplings) for univariate distributions such as the normal, the uniform, and the triangular distribution. We also derive optimal adversarial classifiers in these settings. Our analysis leads to algorithm-independent fundamental limits on adversarial risk, which we calculate for several real-world datasets. We extend our results to general loss functions under convexity and smoothness assumptions.

Key facts. Cited by 36 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 Dec 2019.

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Citing papers per year: 2021: 10; 2022: 9; 2023: 8; 2024: 5; 2025: 2; 2026: 2.

36 papers.

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  1. 2022The Many Faces of Adversarial Riskcited by 28
  2. 2021On the Existence of the Adversarial Bayes Classifier (Extended Version)cited by 25
  3. 2021Mixed Nash Equilibria in the Adversarial Examples Gamecited by 22
  4. 2022The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classificationcited by 21
  5. 2021The Geometry of Adversarial Training in Binary Classificationcited by 20
  6. 2022Existence and Minimax Theorems for Adversarial Surrogate Risks in Binary Classificationcited by 15
  7. 2021Fundamental Tradeoffs in Distributionally Adversarial Trainingcited by 12
  8. 2022Towards Consistency in Adversarial Classificationcited by 12
  9. 2023Adversarial Examples Might be Avoidable: The Role of Data Concentration in Adversarial Robustnesscited by 11
  10. 2021Understanding Generalization in Adversarial Training via the Bias-Variance Decompositioncited by 10
  11. 2022Gamma-convergence of a nonlocal perimeter arising in adversarial machine learningcited by 10
  12. 2023Optimal Transport Perturbations for Safe Reinforcement Learning with Robustness Guaranteescited by 9
24 more
  1. 2023It Is All About Data: A Survey on the Effects of Data on Adversarial Robustnesscited by 9
  2. 2023On the existence of solutions to adversarial training in multiclass classificationcited by 9
  3. 2021Adversarial robustness for latent models: Revisiting the robust-standard accuracies tradeoffcited by 8
  4. 2023Characterizing the Optimal 0-1 Loss for Multi-class Classification with a Test-time Attackercited by 6
  5. 2021Robust Classification Under ℓ0 Attack for the Gaussian Mixture Modelcited by 5
  6. 2022Quantile-constrained Wasserstein projections for robust interpretability of numerical and machine learning modelscited by 4
  7. 2023On adversarial robustness and the use of Wasserstein ascent-descent dynamics to enforce itcited by 4
  8. 2024A mean curvature flow arising in adversarial trainingcited by 4
  9. 2021Fast block-coordinate Frank-Wolfe algorithm for semi-relaxed optimal transportcited by 3
  10. 2024A Notion of Uniqueness for the Adversarial Bayes Classifiercited by 3
  11. 2025Scanning Trojaned Models Using Out-of-Distribution Samplescited by 3
  12. 2023Non-Asymptotic Bounds for Adversarial Excess Risk under Misspecified Modelscited by 2
  13. 2024Adversarial Consistency and the Uniqueness of the Adversarial Bayes Classifiercited by 2
  14. 2024Minimax rates of convergence for nonparametric regression under adversarial attackscited by 2
  15. 2021Lower Bounds on Cross-Entropy Loss in the Presence of Test-time Adversariescited by 1
  16. 2022Eikonal depth: an optimal control approach to statistical depthscited by 1
  17. 2023On Achieving Optimal Adversarial Test Errorcited by 1
  18. 2024Uniform Convergence of Adversarially Robust Classifierscited by 1
  19. 2025Adversarial Surrogate Risk Bounds for Binary Classificationcited by 1
  20. 2021Generalized Likelihood Ratio Test for Adversarially Robust Hypothesis Testingcited by 0
  21. 2022Connecting adversarial attacks and optimal transport for domain adaptationcited by 0
  22. 2022Achieve Optimal Adversarial Accuracy for Adversarial Deep Learning using Stackelberg Gamecited by 0
  23. 2026Certified Robustness from Approximate Gaussian Mixture Structures in Pretrained Latent Spacescited by 0
  24. 2026Statistical Inference for Adversarial Training: Central Limit Theorems via Optimal Transportcited by 0