mlsanityData to 14 Oct 2026

Randomization matters. How to defend against strong adversarial attacks

arXiv 2002.11565 ↗First posted 26 Feb 2020cs.LG cs.CR stat.MLcited by 37

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Abstract (arXiv)

Is there a classifier that ensures optimal robustness against all adversarial attacks? This paper answers this question by adopting a game-theoretic point of view. We show that adversarial attacks and defenses form an infinite zero-sum game where classical results (e.g. Sion theorem) do not apply. We demonstrate the non-existence of a Nash equilibrium in our game when the classifier and the Adversary are both deterministic, hence giving a negative answer to the above question in the deterministic regime. Nonetheless, the question remains open in the randomized regime. We tackle this problem by showing that, undermild conditions on the dataset distribution, any deterministic classifier can be outperformed by a randomized one. This gives arguments for using randomization, and leads us to a new algorithm for building randomized classifiers that are robust to strong adversarial attacks. Empirical results validate our theoretical analysis, and show that our defense method considerably outperforms Adversarial Training against state-of-the-art attacks.

Key facts. Cited by 37 papers in the map (data through 14 Oct 2026). First posted on arXiv 26 Feb 2020.

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Citing papers per year: 2021: 8; 2022: 10; 2023: 9; 2024: 4; 2025: 5; 2026: 1.

37 papers.

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  1. 2022Diffusion Models for Adversarial Purificationcited by 476
  2. 2021Adversarial purification with Score-based generative modelscited by 134
  3. 2023How Does Information Bottleneck Help Deep Learning?cited by 93
  4. 2021A Dynamical System Perspective for Lipschitz Neural Networkscited by 60
  5. 2021Attacking Adversarial Attacks as A Defensecited by 32
  6. 2022The Many Faces of Adversarial Riskcited by 28
  7. 2021Mixed Nash Equilibria in the Adversarial Examples Gamecited by 22
  8. 2023Balance, Imbalance, and Rebalance: Understanding Robust Overfitting from a Minimax Game Perspectivecited by 18
  9. 2023The Best Defense is a Good Offense: Adversarial Augmentation against Adversarial Attackscited by 15
  10. 2022Towards Consistency in Adversarial Classificationcited by 12
  11. 2023Vulnerabilities in Video Quality Assessment Models: The Challenge of Adversarial Attackscited by 12
  12. 2022Building Robust Ensembles via Margin Boostingcited by 8
25 more
  1. 2022Nash Equilibria and Pitfalls of Adversarial Training in Adversarial Robustness Gamescited by 8
  2. 2021The art of defense: letting networks fool the attackercited by 6
  3. 2022Game Theoretic Mixed Experts for Combinational Adversarial Machine Learningcited by 6
  4. 2025Adversarial Training for Defense Against Label Poisoning Attackscited by 6
  5. 2022Adversarial Vulnerability of Randomized Ensemblescited by 5
  6. 2023On the Role of Randomization in Adversarially Robust Classificationcited by 4
  7. 2025Strategic Classification with Randomised Classifierscited by 4
  8. 2021When Should You Defend Your Classifier -- A Game-theoretical Analysis of Countermeasures against Adversarial Examplescited by 3
  9. 2023On the Robustness of Randomized Ensembles to Adversarial Perturbationscited by 3
  10. 2022Towards Evading the Limits of Randomized Smoothing: A Theoretical Analysiscited by 2
  11. 2022Metric-Fair Classifier Derandomizationcited by 2
  12. 2023Do we need entire training data for adversarial training?cited by 1
  13. 2023Adversarial attacks for mixtures of classifierscited by 1
  14. 2024Position: Towards Resilience Against Adversarial Examplescited by 1
  15. 2024Understanding Byzantine Robustness in Federated Learning with A Black-box Servercited by 1
  16. 2021Robustifying ℓ_∞ Adversarial Training to the Union of Perturbation Modelscited by 0
  17. 2021Scalable Optimal Classifiers for Adversarial Settings under Uncertaintycited by 0
  18. 2022Achieve Optimal Adversarial Accuracy for Adversarial Deep Learning using Stackelberg Gamecited by 0
  19. 2023Towards Optimal Randomized Strategies in Adversarial Example Gamecited by 0
  20. 2024LightPure: Realtime Adversarial Image Purification for Mobile Devices Using Diffusion Modelscited by 0
  21. 2024Adversarial Detection with a Dynamically Stable Systemcited by 0
  22. 2025Unveiling the Role of Randomization in Multiclass Adversarial Classification: Insights from Graph Theorycited by 0
  23. 2025Towards provable probabilistic safety for scalable embodied AI systemscited by 0
  24. 2025Lattice Climber Attack: Adversarial attacks for randomized mixtures of classifierscited by 0
  25. 2026Statistical Inference for Adversarial Training: Central Limit Theorems via Optimal Transportcited by 0