Characterizing Adversarial Bayes Classifiers in Binary Classification: Uniqueness, Regularity, and Tradeoffs

The paper proposes new notions of 'uniqueness' and 'equivalence' for adversarial Bayes classifiers in binary classification, and uses these to characterize the structure and properties of adversarial Bayes classifiers, especially in one dimension. This includes identifying necessary conditions for regularity, understanding how regularity improves with the perturbation radius, and illustrating the potential to mitigate the accuracy-robustness tradeoff through careful selection of the adversarial Bayes classifier.