We propose a new notion of uniqueness for the adversarial Bayes classifier in the setting of binary classification. Analyzing this notion of uniqueness 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 notions of regularity improve for adversarial Bayes classifiers. We demonstrate with various examples that the boundary of the adversarial Bayes classifier frequently lies near the boundary of the Bayes classifier.

翻译：我们针对二元分类场景中对抗贝叶斯分类器提出了一种新的唯一性概念。对该唯一性概念的分析产生了一个简单流程，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。随后利用该特征刻画证明：随着扰动半径增大，对抗贝叶斯分类器的某些正则性指标会提升。通过多样化示例验证表明，对抗贝叶斯分类器的决策边界通常位于贝叶斯分类器边界附近。