Social Learning in Community Structured Graphs

Traditional social learning frameworks consider environments with a homogeneous state, where each agent receives observations conditioned on that true state of nature. In this work, we relax this assumption and study the distributed hypothesis testing problem in a heterogeneous environment, where each agent can receive observations conditioned on their own personalized state of nature (or truth). We particularly focus on community structured networks, where each community admits their own true hypothesis. This scenario is common in various contexts, such as when sensors are spatially distributed, or when individuals in a social network have differing views or opinions. We show that the adaptive social learning strategy is a preferred choice for nonstationary environments, and allows each cluster to discover its own truth.