The Role of Memory in Social Learning When Sharing Partial Opinions

In social learning, a group of agents linked by a graph topology collect data and exchange opinions on some topic of interest, represented by a finite set of hypotheses. Traditional social learning algorithms allow all agents in the network to gain full confidence on the true underlying hypothesis as the number of observations increases. Under partial information sharing, agents can exchange opinions only on a single hypothesis. This introduces significant challenges as compared to the standard case of full opinion sharing. We propose a novel strategy where each agent forms a valid belief by completing the partial beliefs received from its neighbors. The completion process exploits the knowledge accumulated in the past beliefs, thanks to a principled memory-aware rule inspired by a Bayesian criterion. We provide a detailed characterization of the memory-aware strategy, which reveals novel learning dynamics and highlights its advantages over previously considered schemes.