|A Game-Theoretic Approach to Sequential Detection in Adversarial Environments
|Ruizhi Zhang, University of Nebraska-Lincoln, United States; Shaofeng Zou, University at Buffalo, the State University of New York, United States
|E.1: Detection Theory
|Detection and Estimation
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|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.