Adversarial training is one of the most popular methods for training methods robust to adversarial attacks, however, it is not well-understood from a theoretical perspective. We prove and existence, regularity, and minimax theorems for adversarial surrogate risks. Our results explain some empirical observations on adversarial robustness from prior work and suggest new directions in algorithm development. Furthermore, our results extend previously known existence and minimax theorems for the adversarial classification risk to surrogate risks.

翻译：对抗训练是提升模型对抗攻击鲁棒性最常用的方法之一，然而其理论理解尚不充分。本文证明了对抗替代风险的存在性、正则性与极小极大定理。我们的结果解释了先前工作中关于对抗鲁棒性的若干实证观察，并为算法开发指明了新方向。此外，我们的结果将先前已知的对抗分类风险存在性定理与极小极大定理推广至替代风险。