On the Role of Randomization in Adversarially Robust Classification

Lucas Gnecco Heredia, Muni Sreenivas Pydi, Laurent Meunier, benjamin negrevergne, Yann Chevaleyre

Keywords: adversarial attacks, robustness, adversarial, attacks, deep learning, randomization, randomized ensembles

TL;DR: We study the conditions under which randomized classifiers offer improvements for adversarial robustness. We show that for any binary randomized classifiers, there exists a deterministic one that is at least as robust.

Abstract:

Deep neural networks are known to be vulnerable to small adversarial perturbations in test data. To defend against adversarial attacks, probabilistic classifiers have been proposed as an alternative to deterministic ones. However, literature has conflicting findings on the effectiveness of probabilistic classifiers in comparison to deterministic ones. In this paper, we clarify the role of randomization in building adversarially robust classifiers.
Given a base hypothesis set of deterministic classifiers, we show the conditions under which a randomized ensemble outperforms the hypothesis set in adversarial risk, extending previous results.
Additionally, we show that for any probabilistic binary classifier (including randomized ensembles), there exists a deterministic classifier that outperforms it. Finally, we give an explicit description of the deterministic hypothesis set that contains such a deterministic classifier for many types of commonly used probabilistic classifiers, *i.e.* randomized ensembles and parametric/input noise injection.

Submission Number: 14593