Towards Consistency in Adversarial Classification

In this paper, we study the problem of consistency in the context of adversarial examples. Specifically, we tackle the following question: can surrogate losses still be used as a proxy for minimizing the 0/1 loss in the presence of an adversary that alters the inputs at test-time? Different from the standard classification task, this question cannot be reduced to a point-wise minimization problem, and calibration needs not to be sufficient to ensure consistency. In this paper, we expose some pathological behaviors specific to the adversarial problem, and show that no convex surrogate loss can be consistent or calibrated in this context. It is therefore necessary to design another class of surrogate functions that can be used to solve the adversarial consistency issue.