We propose a new notion of uniqueness for the adversarial Bayes classifier in the setting of binary classification. Analyzing this concept produces a simple procedure for computing all adversarial Bayes classifiers for a well-motivated family of one dimensional data distributions. This characterization is then leveraged to show that as the perturbation radius increases, certain the regularity of adversarial Bayes classifiers improves. Various examples demonstrate that the boundary of the adversarial Bayes classifier frequently lies near the boundary of the Bayes classifier.

翻译：我们提出一种关于对抗贝叶斯分类器在二分类场景下唯一性的新概念。分析该概念可得一个简单流程，用于计算一类合理的一维数据分布的所有对抗贝叶斯分类器。进而利用这一刻画表明：随着扰动半径增大，对抗贝叶斯分类器的某种正则性会提升。多种实例表明，对抗贝叶斯分类器的边界通常邻近贝叶斯分类器的边界。