Related papers: On the existence of solutions to adversarial training in multiclass classification

On the existence of solutions to adversarial training in multiclass classification

URL: http://arxiv.org/abs/2305.00075v2
Date: Mon, 29 May 2023 06:19:45 GMT
Title: On the existence of solutions to adversarial training in multiclass classification
Authors: Nicolas Garcia Trillos, Matt Jacobs, Jakwang Kim
Abstract summary: We prove the existence of Borel measurable robust classifiers in three models of the problem of adversarial training in multiclass classification. As a corollary to our results, we prove the existence of Borel measurable solutions to the agnostic adversarial training problem in the binary classification setting.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We study three models of the problem of adversarial training in multiclass classification designed to construct robust classifiers against adversarial perturbations of data in the agnostic-classifier setting. We prove the existence of Borel measurable robust classifiers in each model and provide a unified perspective of the adversarial training problem, expanding the connections with optimal transport initiated by the authors in previous work and developing new connections between adversarial training in the multiclass setting and total variation regularization. As a corollary of our results, we prove the existence of Borel measurable solutions to the agnostic adversarial training problem in the binary classification setting, a result that improves results in the literature of adversarial training, where robust classifiers were only known to exist within the enlarged universal $\sigma$-algebra of the feature space.

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