Paper ID: 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

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.

Submitted: Feb 21, 2023