Adversarially robust sequential hypothesis testing. Issue 1 (18th May 2022) - Cao, Shuchen; Zhang, Ruizhi; Zou, Shaofeng
Abstract: The problem of sequential hypothesis testing is studied, where samples are taken sequentially, and the goal is to distinguish between the null hypothesis where the samples are generated according to a distribution p and the alternative hypothesis where the samples are generated according to a distribution q . The defender (decision maker) aims to distinguish the two hypotheses using as few samples as possible subject to false alarm constraints. The problem is studied under the adversarial setting, where the data generating distributions under the two hypotheses are manipulated by an adversary, whose goal is to deteriorate the performance of the defender—for example, increasing the probability of error and expected sample sizes—with minimal cost. Specifically, under the null hypothesis, the adversary picks a distribution p ∈ P with cost c 0 ( p ), and under the alternative hypothesis, the adversary picks a distribution q ∈ Q with cost c 1 ( q ) . This problem is formulated as a non-zero-sum game between the defender and the adversary. A pair of strategies (the adversary's strategy and the defender's strategy) is proposed and proved to be a Nash equilibrium pair for the non-zero-sum game between the adversary and the defender asymptotically. The defender's strategy is a sequential probability ratio test and thus is computationally efficient for practical implementation.