Resilient Distributed Hypothesis Testing with Time-Varying Network Topology

We study the problem of distributed hypothesis testing, where a team of mobile agents aims to agree on the true hypothesis (out of a finite set of hypotheses) that best explains a sequence of their local and possibly noisy observations. The setting requires team collaborations through a time-varying network topology due to mobility and limited communication range. We also assume that there is an unknown subset of compromised agents that may deliberately share wrong information to undermine the team objective. We propose a distributed algorithm where each agent maintains two sets of beliefs (i.e., probability distributions over hypotheses), namely local and actual beliefs. For each agent at each time step, the local belief is updated based on its local observations. Then the actual belief is updated with its local belief and shared actual beliefs from the other agents within the communication range. We show that the actual belief of each non-adversarial agent converges almost surely to the true hypothesis. Unlike most of the existing literature, we guarantee the convergence without a connectivity constraint of the time-varying network topology.