On Proper Learnability between Average- and Worst-case Robustness

Published: 21 Sept 2023, Last Modified: 07 Jan 2024NeurIPS 2023 posterEveryoneRevisionsBibTeX
Keywords: Adversarial Robustness, PAC Learning
TL;DR: We study proper PAC learnability under relaxed notions of adversarial robustness.
Abstract: Recently, Montasser at al. (2019) showed that finite VC dimension is not sufficient for proper adversarially robust PAC learning. In light of this hardness, there is a growing effort to study what type of relaxations to the adversarially robust PAC learning setup can enable proper learnability. In this work, we initiate the study of proper learning under relaxations of the worst-case robust loss. We give a family of robust loss relaxations under which VC classes are properly PAC learnable with sample complexity close to what one would require in the standard PAC learning setup. On the other hand, we show that for an existing and natural relaxation of the worst-case robust loss, finite VC dimension is not sufficient for proper learning. Lastly, we give new generalization guarantees for the adversarially robust empirical risk minimizer.
Supplementary Material: pdf
Submission Number: 5210