On the existence of solutions to adversarial training in multiclass classification

Abstract

Adversarial training is a min-max optimization problem that is designed to construct robust classifiers against adversarial perturbations of data. We study three models of adversarial training in the multiclass 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 their previous work [21]. In addition, we develop new connections between adversarial training in the multiclass setting and total variation regularization. As a corollary of our results, we provide an alternative proof of the existence of Borel measurable solutions to the agnostic adversarial training problem in the binary classification setting.

Keywords

• existence of solutions for minimax problems
• nonparametric robustness
• general topics in artificial intelligence
• problem-solving in the context of artificial intelligence
• 49J35
• 62G35
• 68T20