Multiple-Observation Hypothesis Testing under Adversarial Conditions

We address the problem of binary hypothesis testing based on multiple observations in the presence of an adversary corrupting part or all the observations. We propose a general framework based on game-theory that encompasses a wide variety of situations including distributed detection, data fusion, multimedia forensics, sensor networks. The proposed approach extends the Neyman-Pearson approach to an adversarial setting in which the analyst must ensure that type I error probability stays below a threshold, and the adversary tries to induce a type II error. We derive the equilibrium point of the game in an asymptotic set up, showing that a dominant strategy exists for the analyst. The paper opens the way to further analysis in which the payoff of the game at the equilibrium is analyzed thus permitting to understand the ultimate achievable performance of multiple-observation hypothesis testing under adversarial conditions.