On the robustness of randomized classifiers to adversarial examples
It addresses adversarial attacks for machine learning practitioners by offering theoretical guarantees and practical methods, though it is incremental as it builds on existing randomized classifier concepts.
This paper tackles the problem of adversarial robustness in machine learning by analyzing randomized classifiers, introducing a new robustness definition and providing theoretical bounds and a noise injection method. It achieves state-of-the-art clean accuracy of over 0.82 on CIFAR-10 with guaranteed robust accuracy bounds of 0.45 against specific adversarial attacks.
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).