Self-aware Social Learning over Graphs

TL;DR

This paper introduces a social learning algorithm for self-interested agents over graphs, enabling them to identify their true hypotheses by adaptively collaborating with peers observing the same data, improving learning accuracy.

Contribution

It proposes an adaptive weighting scheme allowing agents to selectively cooperate with peers observing the same hypothesis, enhancing social learning in self-interested settings.

Findings

Agents can correctly identify their true hypotheses asymptotically.

The adaptive scheme improves learning performance over non-cooperative methods.

Theoretical results are validated through numerical simulations.

Abstract

In this paper we study the problem of social learning under multiple true hypotheses and self-interested agents which exchange information over a graph. In this setup, each agent receives data that might be generated from a different hypothesis (or state) than the data other agents receive. In contrast to the related literature in social learning, which focuses on showing that the network achieves consensus, here we study the case where every agent is self-interested and wants to find the hypothesis that generates its own observations. However, agents do not know which ones of their peers wants to find the same state with them and as a result they do not know which agents they should cooperate with. To this end, we propose a scheme with adaptive combination weights and study the consistency of the agents' learning process. The scheme allows each agent to identify and collaborate with neighbors that observe the same hypothesis, while excluding others, thus resulting in improved performance compared to both non-cooperative learning and cooperative social learning solutions. We analyze the asymptotic behavior of agents' beliefs under the proposed social learning algorithm and provide sufficient conditions that enable all agents to correctly identify their true hypotheses. The theoretical analysis is corroborated by numerical simulations.