On the Existence of The Adversarial Bayes Classifier

Pranjal Awasthi, Natalie Frank, Mehryar Mohri

Keywords: Adversarial Learning, Learning Theory, Consistency, Calibration, Bayes classifiers

TL;DR: We prove that in many typical adversarial learning scenarios, there exists a classifier that minimizes the adversarial loss

Abstract: Adversarial robustness is a critical property in a variety of modern machine learning applications. While it has been the subject of several recent theoretical studies, many important questions related to adversarial robustness are still open. In this work, we study a fundamental question regarding Bayes optimality for adversarial robustness. We provide general sufficient conditions under which the existence of a Bayes optimal classifier can be guaranteed for adversarial robustness. Our results can provide a useful tool for a subsequent study of surrogate losses in adversarial robustness and their consistency properties.

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