mlsanityData to 7 Oct 2026

Minimax rates of convergence for nonparametric regression under adversarial attacks

arXiv 2410.09402 ↗First posted 12 Oct 2024math.ST stat.ML stat.THcited by 2

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Abstract (arXiv)

Recent research shows the susceptibility of machine learning models to adversarial attacks, wherein minor but maliciously chosen perturbations of the input can significantly degrade model performance. In this paper, we theoretically analyse the limits of robustness against such adversarial attacks in a nonparametric regression setting, by examining the minimax rates of convergence in an adversarial sup-norm. Our work reveals that the minimax rate under adversarial attacks in the input is the same as sum of two terms: one represents the minimax rate in the standard setting without adversarial attacks, and the other reflects the maximum deviation of the true regression function value within the target function class when subjected to the input perturbations. The optimal rates under the adversarial setup can be achieved by an adversarial plug-in procedure constructed from a minimax optimal estimator in the corresponding standard setting. Two specific examples are given to illustrate the established minimax results.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 37 of its 73 references that are in the map. First posted on arXiv 12 Oct 2024.

Builds on

37 of 73 references.

References · 37

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25 more
  1. 2018Adversarially Robust Generalization Requires More Datacited by 318
  2. 2018Certified Defenses against Adversarial Examplescited by 305
  3. 2018Rademacher Complexity for Adversarially Robust Generalizationcited by 132
  4. 2019Adversarial Training Can Hurt Generalizationcited by 131
  5. 2019VC Classes are Adversarially Robustly Learnable, but Only Improperlycited by 83
  6. 2020Precise Tradeoffs in Adversarial Training for Linear Regressioncited by 76
  7. 2020Distributionally Robust Losses for Latent Covariate Mixturescited by 57
  8. 2019Lower Bounds on Adversarial Robustness from Optimal Transportcited by 52
  9. 2020Precise Statistical Analysis of Classification Accuracies for Adversarial Trainingcited by 49
  10. 2020Adversarial Learning Guarantees for Linear Hypotheses and Neural Networkscited by 47
  11. 2019Scaleable input gradient regularization for adversarial robustnesscited by 45
  12. 2020The Curious Case of Adversarially Robust Models: More Data Can Help, Double Descend, or Hurt Generalizationcited by 39
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  17. 2020Adversarially Robust Estimate and Risk Analysis in Linear Regressioncited by 22
  18. 2022Overparameterized Linear Regression under Adversarial Attackscited by 21
  19. 2020When are Non-Parametric Methods Robust?cited by 15
  20. 2019Robustness for Non-Parametric Classification: A Generic Attack and Defensecited by 12
  21. 2023Robust Nonparametric Regression under Poisoning Attackcited by 11
  22. 2018Sparsity-based Defense against Adversarial Attacks on Linear Classifierscited by 8
  23. 2023Sup-Norm Convergence of Deep Neural Network Estimator for Nonparametric Regression by Adversarial Trainingcited by 6
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  25. 2023Non-Asymptotic Bounds for Adversarial Excess Risk under Misspecified Modelscited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026On damage of interpolation to adversarial robustness in regressioncited by 1
  2. 2026Adversarial Robustness of NTK Neural Networkscited by 0