Online Learning of Dynamic Parameters in Social Networks

TL;DR

This paper introduces online learning algorithms for dynamic social networks where the underlying state evolves randomly, providing bounds on tracking accuracy and analyzing estimator performance.

Contribution

It proposes two update mechanisms for online learning in dynamic social networks and analyzes their effectiveness in tracking the evolving state.

Findings

One estimator achieves optimal mean-square deviation.

Bounded variance in tracking the dynamic state.

Explicit expressions for steady-state estimation error.

Abstract

This paper addresses the problem of online learning in a dynamic setting. We consider a social network in which each individual observes a private signal about the underlying state of the world and communicates with her neighbors at each time period. Unlike many existing approaches, the underlying state is dynamic, and evolves according to a geometric random walk. We view the scenario as an optimization problem where agents aim to learn the true state while suffering the smallest possible loss. Based on the decomposition of the global loss function, we introduce two update mechanisms, each of which generates an estimate of the true state. We establish a tight bound on the rate of change of the underlying state, under which individuals can track the parameter with a bounded variance. Then, we characterize explicit expressions for the steady state mean-square deviation(MSD) of the estimates from the truth, per individual. We observe that only one of the estimators recovers the optimal MSD, which underscores the impact of the objective function decomposition on the learning quality. Finally, we provide an upper bound on the regret of the proposed methods, measured as an average of errors in estimating the parameter in a finite time.