mlsanityData to 14 Oct 2026

Nash Equilibria and Pitfalls of Adversarial Training in Adversarial Robustness Games

arXiv 2210.12606 ↗First posted 23 Oct 2022cs.LG cs.GTcited by 8

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Abstract (arXiv)

Adversarial training is a standard technique for training adversarially robust models. In this paper, we study adversarial training as an alternating best-response strategy in a 2-player zero-sum game. We prove that even in a simple scenario of a linear classifier and a statistical model that abstracts robust vs. non-robust features, the alternating best response strategy of such game may not converge. On the other hand, a unique pure Nash equilibrium of the game exists and is provably robust. We support our theoretical results with experiments, showing the non-convergence of adversarial training and the robustness of Nash equilibrium.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 40 of its 59 references that are in the map. First posted on arXiv 23 Oct 2022.

Builds on

40 of 59 references.

References · 40

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2014Explaining and Harnessing Adversarial Examplescited by 7,364
  3. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,415
  4. 2013Intriguing properties of neural networkscited by 5,155
  5. 2019Theoretically Principled Trade-off between Robustness and Accuracycited by 1,517
  6. 2019Certified Adversarial Robustness via Randomized Smoothingcited by 1,340
  7. 2019Adversarial Examples Are Not Bugs, They Are Featurescited by 953
  8. 2018Robustness May Be at Odds with Accuracycited by 880
  9. 2017Ensemble Adversarial Training: Attacks and Defensescited by 840
  10. 2020Fast is better than free: Revisiting adversarial trainingcited by 727
  11. 2019Adversarial Training for Free!cited by 643
  12. 2020Overfitting in adversarially robust deep learningcited by 506
28 more
  1. 2019Unlabeled Data Improves Adversarial Robustnesscited by 416
  2. 2018Adversarially Robust Generalization Requires More Datacited by 318
  3. 2018Feature Denoising for Improving Adversarial Robustnesscited by 314
  4. 2021Improving Robustness using Generated Datacited by 234
  5. 2019Improving Adversarial Robustness via Promoting Ensemble Diversitycited by 213
  6. 2021Data Augmentation Can Improve Robustnesscited by 194
  7. 2021A Universal Law of Robustness via Isoperimetrycited by 151
  8. 2015Fast Convergence of Regularized Learning in Gamescited by 150
  9. 2020Understanding and Mitigating the Tradeoff Between Robustness and Accuracycited by 149
  10. 2019Adversarial Robustness through Local Linearizationcited by 146
  11. 2017Cycles in adversarial regularized learningcited by 124
  12. 2021Robust Learning Meets Generative Models: Can Proxy Distributions Improve Adversarial Robustness?cited by 113
  13. 2020Feature Purification: How Adversarial Training Performs Robust Deep Learningcited by 107
  14. 2020Precise Tradeoffs in Adversarial Training for Linear Regressioncited by 77
  15. 2019Adversarially Robust Generalization Just Requires More Unlabeled Datacited by 76
  16. 2020A law of robustness for two-layers neural networkscited by 55
  17. 2020Randomization matters. How to defend against strong adversarial attackscited by 37
  18. 2020Adversarial Example Gamescited by 34
  19. 2019Online Non-Convex Learning: Following the Perturbed Leader is Optimalcited by 32
  20. 2020EMPIR: Ensembles of Mixed Precision Deep Networks for Increased Robustness against Adversarial Attackscited by 28
  21. 2021Adversarial Examples in Multi-Layer Random ReLU Networkscited by 26
  22. 2020Improving Adversarial Robustness via Unlabeled Out-of-Domain Datacited by 23
  23. 2021Mixed Nash Equilibria in the Adversarial Examples Gamecited by 22
  24. 2020A Game Theoretic Analysis of Additive Adversarial Attacks and Defensescited by 21
  25. 2016Randomized Prediction Games for Adversarial Machine Learningcited by 11
  26. 2022Building Robust Ensembles via Margin Boostingcited by 8
  27. 2019Robust Attacks against Multiple Classifierscited by 7
  28. 2019Pure Nash Equilibria and Best-Response Dynamics in Random Gamescited by 4

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 1; 2023: 4; 2024: 2; 2025: 0; 2026: 1.

8 papers.

  1. 2023Balance, Imbalance, and Rebalance: Understanding Robust Overfitting from a Minimax Game Perspectivecited by 18
  2. 2023Reliable learning in challenging environmentscited by 10
  3. 2023On the existence of solutions to adversarial training in multiclass classificationcited by 9
  4. 2022Game Theoretic Mixed Experts for Combinational Adversarial Machine Learningcited by 6
  5. 2023Responsible AI (RAI) Games and Ensemblescited by 1
  6. 2024Paths to Equilibrium in Gamescited by 1
  7. 2024Position: Towards Resilience Against Adversarial Examplescited by 1
  8. 2026Statistical Inference for Adversarial Training: Central Limit Theorems via Optimal Transportcited by 0