  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.
