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arXiv · 2302.10722

Characterizing the Optimal 0-1 Loss for Multi-class Classification with a Test-time Attacker

Sihui Dai·Wenxin Ding·Arjun Nitin Bhagoji·Daniel Cullina·Ben Y. Zhao·Haitao Zheng·Prateek Mittal
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Abstract

Finding classifiers robust to adversarial examples is critical for their safe deployment. Determining the robustness of the best possible classifier under a given threat model for a given data distribution and comparing it to that achieved by state-of-the-art training methods is thus an important diagnostic tool. In this paper, we find achievable information-theoretic lower bounds on loss in the presence of a test-time attacker for multi-class classifiers on any discrete dataset. We provide a general framework for finding the optimal 0-1 loss that revolves around the construction of a conflict hypergraph from the data and adversarial constraints. We further define other variants of the attacker-classifier game that determine the range of the optimal loss more efficiently than the full-fledged hypergraph construction. Our evaluation shows, for the first time, an analysis of the gap to optimal robustness for classifiers in the multi-class setting on benchmark datasets.

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Sihui Dai, Wenxin Ding, Arjun Nitin Bhagoji, Daniel Cullina, Ben Y. Zhao, Haitao Zheng, Prateek Mittal. 2023-12-06. Characterizing the Optimal 0-1 Loss for Multi-class Classification with a Test-time Attacker. https://arxiv.org/abs/2302.10722

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