Multiple Hypothesis Testing in Adversarial Environments: A Game-theoretic Approach

This paper considers hypothesis testing using multiple sensors, among which some might be compromised and send arbitrary data. There exist no less than two hypotheses, which is an extension of the binary hypothesis testing in our recent work [1]. The exponent rate, under which the worst-case probability of detection error goes to zero, is adopted as the performance metric. The problem is formulated in a game theoretic way and an equilibrium pair of attack and detection strategies is given. We also provide a simplified equilibrium detection algorithm when the mean of Gaussian noises is to be determined. Two extensions are also studied and a Nash equilibrium is provided for each case using a similar methodology. In the first extension, composite hypothesis testing is studied, i.e., the distribution of observations under each hypothesis is not known exactly but is characterized by a (unknown) parameter. In the second one, heterogeneous sensors are used to collect measurements.