Multivariate Belief Formation for Distributed Multitask Learning

In traditional social learning, a network of agents wish to learn a common truth or hypothesis. However, in many real-world applications, different agents may observe data related to different hypotheses, resulting in clusters or communities within the network. This setting gives rise to a multitask decisionmaking (MDM) problem. Existing MDM approaches primarily modify the network topology to reflect the community structures, limiting each agent's interactions to its local cluster. While effective, this philosophy imposes strict neighborhood-based identifiability conditions on the agents. This work shows that an alternative approach to solve the decision-making problem with almost-sure guarantees goes in the opposite direction. Instead of becoming self-interested, each agent should be curious about all the truths co-existing in the network. We prove that when the agents know the number of clusters, they almost surely learn the true states of all agents.