Asynchronous Adaptation and Learning over Networks - Part III: Comparison Analysis

TL;DR

This paper demonstrates that asynchronous adaptive networks maintain performance comparable to synchronous and centralized solutions, showing resilience to random failures and minimal impact of asynchrony on convergence rates.

Contribution

It provides a comprehensive comparison analysis showing asynchronous networks perform nearly as well as synchronous and centralized methods, with robustness to random network events.

Findings

Asynchronous adaptation does not degrade convergence rates or asymptotic bias.

Steady-state mean-square deviation slightly increases with small step-sizes.

Distributed networks match centralized solution performance.

Abstract

In Part II [3] we carried out a detailed mean-square-error analysis of the performance of asynchronous adaptation and learning over networks under a fairly general model for asynchronous events including random topologies, random link failures, random data arrival times, and agents turning on and off randomly. In this Part III, we compare the performance of synchronous and asynchronous networks. We also compare the performance of decentralized adaptation against centralized stochastic-gradient (batch) solutions. Two interesting conclusions stand out. First, the results establish that the performance of adaptive networks is largely immune to the effect of asynchronous events: the mean and mean-square convergence rates and the asymptotic bias values are not degraded relative to synchronous or centralized implementations. Only the steady-state mean-square-deviation suffers a degradation in the order of $\nu$, which represents the small step-size parameters used for adaptation. Second, the results show that the adaptive distributed network matches the performance of the centralized solution. These conclusions highlight another critical benefit of cooperation by networked agents: cooperation does not only enhance performance in comparison to stand-alone single-agent processing, but it also endows the network with remarkable resilience to various forms of random failure events and is able to deliver performance that is as powerful as batch solutions.