Distributed Learning over Noisy Communication Networks

TL;DR

This paper investigates how noisy communication channels affect distributed binary coordination games on graphs, analyzing different regimes and providing insights into the impact of communication reliability on learning dynamics and coordination outcomes.

Contribution

It offers a structural analysis of learning dynamics over noisy channels, introduces a finite communication budget model, and connects communication theory with coordination game analysis.

Findings

Fast-communication regime results in Gibbs sampler dynamics scaled by channel reliability.

Snapshot regime's Markov chain is nonreversible but approximates the fast Gibbs sampler at high temperature.

Numerical experiments demonstrate the tradeoff between communication resources and coordination quality.

Abstract

We study binary coordination games over graphs under log-linear learning when neighbor actions are conveyed through explicit noisy communication links. Each edge is modeled as either a binary symmetric channel (BSC) or a binary erasure channel (BEC). We analyze two operational regimes. For binary symmetric and binary erasure channels, we provide a structural characterization of the induced learning dynamics. In a fast-communication regime, agents update using channel-averaged payoffs; the resulting learning dynamics coincide with a Gibbs sampler for a scaled coordination potential, where channel reliability enters only through a scalar attenuation coefficient. In a snapshot regime, agents update from a single noisy realization and ignore channel statistics; the induced Markov chain is generally nonreversible, but admits a high-temperature expansion whose drift matches that of the fast Gibbs sampler with the same attenuation. We further formalize a finite-$K$ communication budget, which interpolates between snapshot and fast behavior as the number of channel uses per update grows. This viewpoint yields a communication-theoretic interpretation in terms of retransmissions and repetition coding, and extends naturally to heterogeneous link reliabilities via effective edge weights. Numerical experiments illustrate the theory and quantify the tradeoff between communication resources and steady-state coordination quality.