Paper Info
Title
On the robustness of randomized classifiers to adversarial examples
Abstract
This paper investigates the theory of robustness against adversarial attacks. We focus on randomized classifiers (i.e. classifiers that output random variables) and provide a thorough analysis of their behavior through the lens of statistical learning theory and information theory. To this aim, we introduce a new notion of robustness for randomized classifiers, enforcing local Lipschitzness using probability metrics. Equipped with this definition, we make two new contributions. The first one consists in devising a new upper bound on the adversarial generalization gap of randomized classifiers. More precisely, we devise bounds on the generalization gap and the adversarial gap i.e. the gap between the risk and the worst-case risk under attack) of randomized classifiers. The second contribution presents a yet simple but efficient noise injection method to design robust randomized classifiers. We show that our results are applicable to a wide range of machine learning models under mild hypotheses. We further corroborate our findings with experimental results using deep neural networks on standard image datasets, namely CIFAR-10 and CIFAR-100. On these tasks, we manage to design robust models that simultaneously achieve state-of-the-art accuracy (over 0.82 clean accuracy on CIFAR-10) and enjoy guaranteed robust accuracy bounds (0.45 against $$\ell _{2}$$ adversaries with magnitude 0.5 on CIFAR-10).
Year
DOI
Venue
2022
10.1007/s10994-022-06216-6
Machine Learning
Keywords
DocType
Volume
Adversarial examples, Randomized classifier, Adversarial generalization gap, Information theory, Randomized smoothing
Journal
111
Issue
ISSN
Citations 
9
0885-6125
0
PageRank 
References 
Authors
0.34
10
6
Name
Order
Citations
PageRank
Rafael Pinot132.05
Meunier, Laurent222.05
Florian Yger3164.42
Cédric Gouy-Pailler46210.69
Yann Chevaleyre584861.76
Jamal Atif630929.49