A Game-Theoretic Approach to Sequential Detection in Adversarial Environments
Ruizhi Zhang, Shaofeng Zou · 2020
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 ∈ 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.