Efficiently Learning Adversarially Robust Halfspaces with Noise

TL;DR

This paper investigates the conditions under which halfspaces can be efficiently learned to be robust against adversarial perturbations, providing algorithms and theoretical insights in noisy and noise-free settings.

Contribution

It offers necessary and sufficient conditions for robust learnability of halfspaces and introduces an efficient algorithm for noisy scenarios with lp-perturbations.

Findings

Characterizes conditions for robust learnability of halfspaces.

Provides an efficient algorithm for noisy lp-perturbation settings.

Establishes theoretical bounds for adversarial robustness.

Abstract

We study the problem of learning adversarially robust halfspaces in the distribution-independent setting. In the realizable setting, we provide necessary and sufficient conditions on the adversarial perturbation sets under which halfspaces are efficiently robustly learnable. In the presence of random label noise, we give a simple computationally efficient algorithm for this problem with respect to any $\ell_p$-perturbation.