Adversarial Consistency and the Uniqueness of the Adversarial Bayes Classifier
This addresses a foundational issue in robust machine learning for researchers and practitioners, though it is incremental as it builds on prior work on adversarial consistency.
The paper tackles the problem of statistical inconsistency in adversarial learning with convex surrogate losses, showing that consistency is equivalent to a uniqueness property of the adversarial Bayes classifier under reasonable distributional assumptions.
Minimizing an adversarial surrogate risk 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 adversarial Bayes classifiers. Specifically, under reasonable distributional assumptions, a convex surrogate loss is statistically consistent for adversarial learning iff the adversarial Bayes classifier satisfies a certain notion of uniqueness.