The worst-case training principle that minimizes the maximal adversarial loss, also known as adversarial training (AT), has shown to be a state-of-the-art approach for enhancing adversarial robustness against norm-ball bounded input perturbations. Nonetheless, min-max optimization beyond the purpose of AT has not been rigorously explored in the research of adversarial attack and defense. In particular, given a set of risk sources (domains), minimizing the maximal loss induced from the domain set can be reformulated as a general min-max problem that is different from AT, since the maximization is taken over the probability simplex of the domain set. Examples of this general formulation include attacking model ensembles, devising universal perturbation to input samples or data transformations, and generalized AT over multiple norm-ball threat models. We show that these problems can be solved under a unified and theoretically principled min-max optimization framework. Our proposed approach leads to substantial performance improvement over the uniform averaging strategy in four different tasks. Moreover, we show how the self-adjusted weighting factors of the probability simplex from our proposed algorithms can be used to explain the importance of different attack and defense models.

本文利用多域最小最大优化的一般性框架，推进了不同类型的对抗性攻击设计，并展示了该统一框架在攻击目标函数，抵御多输入下的统一扰动，生成攻击和数据变换下的对抗攻击等方面的优异性能和整体性工具的作用。

通过最小值最大化优化实现的敌对攻击生成