A Game-Theoretic Approach to Sequential Detection in Adversarial Environments

Abstract

The problem of sequential binary hypothesis testing in an adversarial environment is investigated. Specifically, if there is no adversary, the samples are generated independently by a distribution p; and if the adversary is present, the samples are generated independently by another distribution q. The adversary picks a distribution $q \in \mathcal{Q}$ with cost c(q). The goal of the defender is to decide whether there is an adversary using samples as few as possible; and the goal of the adversary is to fool the defender. The problem is formulated as a non-zero-sum game between the adversary and the defender. A pair of strategies (attack strategy from the adversary and the sequential hypothesis testing scheme from the detector) is proposed and proved to be a Nash equilibrium pair for the non-zero-sum game asymptotically. Numerical experiments are provided to validate our results.