论文标题
$ m $ $ y-ary顺序对抗假设测试游戏的渐近纳什均衡
Asymptotic Nash Equilibrium for the $M$-ary Sequential Adversarial Hypothesis Testing Game
论文作者
论文摘要
在本文中，我们考虑了一个新颖的$ m $ $ mar序列假设测试问题，其中存在对手，并在决策者观察到它们之前将样本的分布删除。该问题被提出为决策者和对手之间在决策者和对手之间进行的顺序对抗性假设测试游戏。该游戏是零和战略性的。我们假设对手在\ emph {All}假设下具有活性，并且知道观察到的样品的基本分布。我们采用了这个框架，因为从决策者的角度来看，这是最坏的情况。决策者的目的是最大程度地减少停止时间的期望，以确保测试尽可能高效；相反，对手的目标是最大化停止时间。我们得出了一对策略，在这些策略下，达到了游戏的渐近纳什均衡。我们还考虑了对手不知道基本假设的情况，因此无论哪种假设有生效，都将被限制应用于相同的策略。数值结果证实了我们的理论发现。
In this paper, we consider a novel $M$-ary sequential hypothesis testing problem in which an adversary is present and perturbs the distributions of the samples before the decision maker observes them. This problem is formulated as a sequential adversarial hypothesis testing game played between the decision maker and the adversary. This game is a zero-sum and strategic one. We assume the adversary is active under \emph{all} hypotheses and knows the underlying distribution of observed samples. We adopt this framework as it is the worst-case scenario from the perspective of the decision maker. The goal of the decision maker is to minimize the expectation of the stopping time to ensure that the test is as efficient as possible; the adversary's goal is, instead, to maximize the stopping time. We derive a pair of strategies under which the asymptotic Nash equilibrium of the game is attained. We also consider the case in which the adversary is not aware of the underlying hypothesis and hence is constrained to apply the same strategy regardless of which hypothesis is in effect. Numerical results corroborate our theoretical findings.
