mlsanityData to 7 Oct 2026

Mixed Nash Equilibria in the Adversarial Examples Game

arXiv 2102.06905 ↗First posted 13 Feb 2021cs.GT cs.CR cs.LGcited by 22

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Abstract (arXiv)

This paper tackles the problem of adversarial examples from a game theoretic point of view. We study the open question of the existence of mixed Nash equilibria in the zero-sum game formed by the attacker and the classifier. While previous works usually allow only one player to use randomized strategies, we show the necessity of considering randomization for both the classifier and the attacker. We demonstrate that this game has no duality gap, meaning that it always admits approximate Nash equilibria. We also provide the first optimization algorithms to learn a mixture of classifiers that approximately realizes the value of this game, i.e. procedures to build an optimally robust randomized classifier.

Key facts. Cited by 22 papers in the map (data through 7 Oct 2026). Builds on 33 of its 45 references that are in the map. First posted on arXiv 13 Feb 2021.

Builds on

33 of 45 references.

References · 33

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
  3. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
  4. 2013Intriguing properties of neural networkscited by 5,114
  5. 2016Wide Residual Networkscited by 3,057
  6. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  7. 2016Adversarial examples in the physical worldcited by 1,762
  8. 2019Theoretically Principled Trade-off between Robustness and Accuracycited by 1,510
  9. 2020Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attackscited by 1,442
  10. 2019Certified Adversarial Robustness via Randomized Smoothingcited by 1,324
  11. 2017Evasion Attacks against Machine Learning at Test Timecited by 686
  12. 2017Adversarial Examples Are Not Easily Detected: Bypassing Ten Detection Methodscited by 542
21 more
  1. 2020Overfitting in adversarially robust deep learningcited by 504
  2. 2016Transferability in Machine Learning: from Phenomena to Black-Box Attacks using Adversarial Samplescited by 439
  3. 2019Unlabeled Data Improves Adversarial Robustnesscited by 415
  4. 2017Mitigating Adversarial Effects Through Randomizationcited by 382
  5. 2017Certifying Some Distributional Robustness with Principled Adversarial Trainingcited by 333
  6. 2020Uncovering the Limits of Adversarial Training against Norm-Bounded Adversarial Examplescited by 275
  7. 2018Robustness via curvature regularization, and vice versacited by 174
  8. 2018Stochastic Activation Pruning for Robust Adversarial Defensecited by 171
  9. 2017The Space of Transferable Adversarial Examplescited by 156
  10. 2019Lower Bounds on Adversarial Robustness from Optimal Transportcited by 52
  11. 2020Randomization matters. How to defend against strong adversarial attackscited by 37
  12. 2019Adversarial Risk via Optimal Transport and Optimal Couplingscited by 36
  13. 2020Calibrated Surrogate Losses for Adversarially Robust Classificationcited by 36
  14. 2020Adversarial Example Gamescited by 34
  15. 2019Theoretical evidence for adversarial robustness through randomizationcited by 33
  16. 2018Theoretical Analysis of Adversarial Learning: A Minimax Approachcited by 31
  17. 2020On Linear Optimization over Wasserstein Ballscited by 23
  18. 2018ResNets Ensemble via the Feynman-Kac Formalism to Improve Natural and Robust Accuraciescited by 18
  19. 2016Randomized Prediction Games for Adversarial Machine Learningcited by 11
  20. 2019Robust Attacks against Multiple Classifierscited by 7
  21. 2018Monge blunts Bayes: Hardness Results for Adversarial Trainingcited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 9; 2023: 7; 2024: 2; 2025: 2; 2026: 1.

22 papers.

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  1. 2022The Many Faces of Adversarial Riskcited by 28
  2. 2022The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classificationcited by 21
  3. 2021The Geometry of Adversarial Training in Binary Classificationcited by 20
  4. 2022Towards Consistency in Adversarial Classificationcited by 12
  5. 2022On the Role of Generalization in Transferability of Adversarial Examplescited by 9
  6. 2023On the existence of solutions to adversarial training in multiclass classificationcited by 9
  7. 2022Nash Equilibria and Pitfalls of Adversarial Training in Adversarial Robustness Gamescited by 8
  8. 2023PubDef: Defending Against Transfer Attacks From Public Modelscited by 7
  9. 2022Game Theoretic Mixed Experts for Combinational Adversarial Machine Learningcited by 6
  10. 2022Adversarial Vulnerability of Randomized Ensemblescited by 5
  11. 2023On adversarial robustness and the use of Wasserstein ascent-descent dynamics to enforce itcited by 4
  12. 2023On the Role of Randomization in Adversarially Robust Classificationcited by 4
10 more
  1. 2022Universal Adversarial Directionscited by 1
  2. 2023Adversarial attacks for mixtures of classifierscited by 1
  3. 2023Responsible AI (RAI) Games and Ensemblescited by 1
  4. 2024Position: Towards Resilience Against Adversarial Examplescited by 1
  5. 2024Understanding Byzantine Robustness in Federated Learning with A Black-box Servercited by 1
  6. 2022Achieve Optimal Adversarial Accuracy for Adversarial Deep Learning using Stackelberg Gamecited by 0
  7. 2023Towards Optimal Randomized Strategies in Adversarial Example Gamecited by 0
  8. 2025Unveiling the Role of Randomization in Multiclass Adversarial Classification: Insights from Graph Theorycited by 0
  9. 2025Lattice Climber Attack: Adversarial attacks for randomized mixtures of classifierscited by 0
  10. 2026Statistical Inference for Adversarial Training: Central Limit Theorems via Optimal Transportcited by 0