On the robustness of randomized classifiers to adversarial examples

• URL: http://arxiv.org/abs/2102.10875v1
• Date: Mon, 22 Feb 2021 10:16:58 GMT
• Title: On the robustness of randomized classifiers to adversarial examples
• Authors: Rafael Pinot and Laurent Meunier and Florian Yger and C\'edric Gouy-Pailler and Yann Chevaleyre and Jamal Atif
• Abstract summary: We introduce a new notion of robustness for randomized classifiers, enforcing local Lipschitzness using probability metrics. We show that our results are applicable to a wide range of machine learning models under mild hypotheses. All robust models we trained models can simultaneously achieve state-of-the-art accuracy.
• Score: 11.359085303200981
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper investigates the theory of robustness against adversarial attacks. We focus on randomized classifiers (\emph{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 (\emph{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. All robust models we trained models can simultaneously achieve state-of-the-art accuracy (over $0.82$ clean accuracy on CIFAR-10) and enjoy \emph{guaranteed} robust accuracy bounds ($0.45$ against $\ell_2$ adversaries with magnitude $0.5$ on CIFAR-10).

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