mlsanityData to 7 Oct 2026

Existence and Minimax Theorems for Adversarial Surrogate Risks in Binary Classification

arXiv 2206.09098 ↗First posted 18 Jun 2022cs.LG math.ST stat.THcited by 15

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Abstract (arXiv)

Adversarial training is one of the most popular methods for training methods robust to adversarial attacks, however, it is not well-understood from a theoretical perspective. We prove and existence, regularity, and minimax theorems for adversarial surrogate risks. Our results explain some empirical observations on adversarial robustness from prior work and suggest new directions in algorithm development. Furthermore, our results extend previously known existence and minimax theorems for the adversarial classification risk to surrogate risks.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). Builds on 31 of its 68 references that are in the map. First posted on arXiv 18 Jun 2022.

Builds on

31 of 68 references.

References · 31

  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. 2017BadNets: Identifying Vulnerabilities in the Machine Learning Model Supply Chaincited by 1,052
  5. 2016Adversarial Machine Learning at Scalecited by 934
  6. 2020Fast is better than free: Revisiting adversarial trainingcited by 723
  7. 2017Evasion Attacks against Machine Learning at Test Timecited by 686
  8. 2019Adversarial Training for Free!cited by 638
  9. 2018Feature Denoising for Improving Adversarial Robustnesscited by 312
  10. 2017Improving the Adversarial Robustness and Interpretability of Deep Neural Networks by Regularizing their Input Gradientscited by 236
  11. 2018Adversarial Logit Pairingcited by 224
  12. 2018Robustness via curvature regularization, and vice versacited by 174
19 more
  1. 2017The Space of Transferable Adversarial Examplescited by 156
  2. 2019A Unified Analysis of Extra-gradient and Optimistic Gradient Methods for Saddle Point Problems: Proximal Point Approachcited by 142
  3. 2021On the Convergence and Robustness of Adversarial Trainingcited by 127
  4. 2019Wasserstein Adversarial Examples via Projected Sinkhorn Iterationscited by 89
  5. 2018Improving DNN Robustness to Adversarial Attacks using Jacobian Regularizationcited by 88
  6. 2019Lower Bounds on Adversarial Robustness from Optimal Transportcited by 52
  7. 2021Calibration and Consistency of Adversarial Surrogate Lossescited by 47
  8. 2019Adversarial Risk via Optimal Transport and Optimal Couplingscited by 36
  9. 2020Calibrated Surrogate Losses for Adversarially Robust Classificationcited by 36
  10. 2022The Many Faces of Adversarial Riskcited by 28
  11. 2020Stronger and Faster Wasserstein Adversarial Attackscited by 25
  12. 2021On the Existence of the Adversarial Bayes Classifier (Extended Version)cited by 25
  13. 2022The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classificationcited by 21
  14. 2021The Geometry of Adversarial Training in Binary Classificationcited by 20
  15. 2020Adversarial Classification: Necessary conditions and geometric flowscited by 19
  16. 2019Robustness for Non-Parametric Classification: A Generic Attack and Defensecited by 12
  17. 2022Towards Consistency in Adversarial Classificationcited by 12
  18. 2016Are Accuracy and Robustness Correlated?cited by 11
  19. 2018Interpreting Adversarial Robustness: A View from Decision Surface in Input Spacecited by 10

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 7; 2024: 4; 2025: 3; 2026: 1.

15 papers.

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  1. 2023On the existence of solutions to adversarial training in multiclass classificationcited by 9
  2. 2023The Adversarial Consistency of Surrogate Risks for Binary Classificationcited by 6
  3. 2023On adversarial robustness and the use of Wasserstein ascent-descent dynamics to enforce itcited by 4
  4. 2023On the Role of Randomization in Adversarially Robust Classificationcited by 4
  5. 2023A minimax optimal control approach for robust neural ODEscited by 4
  6. 2023It begins with a boundary: A geometric view on probabilistically robust learningcited by 3
  7. 2024A Notion of Uniqueness for the Adversarial Bayes Classifiercited by 3
  8. 2023Non-Asymptotic Bounds for Adversarial Excess Risk under Misspecified Modelscited by 2
  9. 2024Adversarial Consistency and the Uniqueness of the Adversarial Bayes Classifiercited by 2
  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
3 more
  1. 2024Distributionally and Adversarially Robust Logistic Regression via Intersecting Wasserstein Ballscited by 0
  2. 2025Unveiling the Role of Randomization in Multiclass Adversarial Classification: Insights from Graph Theorycited by 0
  3. 2026Statistical Inference for Adversarial Training: Central Limit Theorems via Optimal Transportcited by 0