Adversarial training is a common technique for learning robust classifiers.
Prior work showed that convex surrogate losses are not statistically consistent
in the adversarial context -- or in other words, a minimizing sequence of the
adversarial surrogate risk will not necessarily minimize the adversarial
classification error. We connect the consistency of adversarial surrogate
losses to properties of minimizers to the adversarial classification risk,
known as \emph{adversarial Bayes classifiers}. Specifically, under reasonable
distributional assumptions, a convex loss is statistically consistent for
adversarial learning iff the adversarial Bayes classifier satisfies a certain
notion of uniqueness.

对抗训练是学习鲁棒分类器的一种常见技术，先前的研究表明凸代理损失在对抗情景下不具备统计一致性，即对抗代理风险的最小化序列不一定能最小化对抗分类误差。我们将对抗代理损失的一致性与对抗分类风险最小化者的属性联系起来，即所谓的 “对抗贝叶斯分类器”。具体而言，根据合理的分布假设，对抗学习的凸损失仅在对抗贝叶斯分类器满足某种独特性的情况下具备统计一致性。