Adversarial learning guarantees for linear hypotheses and neural networks

Pranjal Awasthi, Natalie S. Frank, Mehryar Mohri

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Adversarial or test time robustness measures the susceptibility of a classifier to perturbations to the test input. While there has been a flurry of recent work on designing defenses against such perturbations, the theory of adversarial robustness is not well understood. In order to make progress on this, we focus on the problem of understanding generalization in adversarial settings, via the lens of Rademacher complexity. We give upper and lower bounds for the adversarial empirical Rademacher complexity of linear hypotheses with adversarial perturbations measured in lr-norm for an arbitrary r C 1. We then extend our analysis to provide Rademacher complexity lower and upper bounds for a single ReLU unit. Finally, we give adversarial Rademacher complexity bounds for feed-forward neural networks with one hidden layer.

Original languageEnglish (US)
Title of host publication37th International Conference on Machine Learning, ICML 2020
EditorsHal Daume, Aarti Singh
PublisherInternational Machine Learning Society (IMLS)
Pages408-418
Number of pages11
ISBN (Electronic)9781713821120
StatePublished - 2020
Event37th International Conference on Machine Learning, ICML 2020 - Virtual, Online
Duration: Jul 13 2020Jul 18 2020

Publication series

Name37th International Conference on Machine Learning, ICML 2020
VolumePartF168147-1

Conference

Conference37th International Conference on Machine Learning, ICML 2020
CityVirtual, Online
Period7/13/207/18/20

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Human-Computer Interaction
  • Software

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