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.


Ruizhi Zhang

University of Nebraska-Lincoln

Shaofeng Zou

University at Buffalo, the State University of New York
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In your literature survey, you may have missed a relevant paper that is stronger than Barni & Tondi (2013): B. Tondi, N. Merhav and M. Barni, ``Detection games under fully active adversaries,'' Entropy, 2019, 21(1), 23; doi: 10.3390/e21010023, special issue on Probabilistic Methods in Information Theory, Hypothesis Testing, and Coding, published on December 29, 2018.
Asked by Neri Merhav - 1135 on Jun 21, 2020. 1 person subscribed to this question.

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Session Chair

Ali Tajer

Rensselaer Polytechnic Institute