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arXiv · 2305.09956

The Adversarial Consistency of Surrogate Risks for Binary Classification

Natalie Frank·Jonathan Niles-Weed
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Abstract

We study the consistency of surrogate risks for robust binary classification. It is common to learn robust classifiers by adversarial training, which seeks to minimize the expected $0$-$1$ loss when each example can be maliciously corrupted within a small ball. We give a simple and complete characterization of the set of surrogate loss functions that are \emph{consistent}, i.e., that can replace the $0$-$1$ loss without affecting the minimizing sequences of the original adversarial risk, for any data distribution. We also prove a quantitative version of adversarial consistency for the $\rho$-margin loss. Our results reveal that the class of adversarially consistent surrogates is substantially smaller than in the standard setting, where many common surrogates are known to be consistent.

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Natalie Frank, Jonathan Niles-Weed. 2023-05-17. The Adversarial Consistency of Surrogate Risks for Binary Classification. https://arxiv.org/abs/2305.09956

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