Social Learning under Randomized Collaborations

TL;DR

This paper analyzes a social learning model where agents randomly select neighbors for information exchange, demonstrating that even with sparse communication, agents reliably learn the truth at the same rate as more resource-intensive methods.

Contribution

It introduces a randomized neighbor selection scheme in social learning, proving convergence to the truth and deriving large deviation estimates for belief updates.

Findings

Agents learn the truth eventually under sparse communication.

Asymptotic convergence rate matches standard algorithms.

Large deviation estimates for belief ratios are derived.

Abstract

We study a social learning scheme where at every time instant, each agent chooses to receive information from one of its neighbors at random. We show that under this sparser communication scheme, the agents learn the truth eventually and the asymptotic convergence rate remains the same as the standard algorithms which use more communication resources. We also derive large deviation estimates of the log-belief ratios for a special case where each agent replaces its belief with that of the chosen neighbor.