On the Learning Behavior of Adaptive Networks - Part II: Performance Analysis

TL;DR

This paper analyzes the steady-state performance of adaptive networks, showing how network topology and operation influence agent performance and demonstrating that distributed networks can match centralized strategies in the small step-size regime.

Contribution

It characterizes the steady-state performance of distributed learning in networks and reveals the equalization effect and conditions for matching centralized performance.

Findings

Network induces performance equalization across agents.

In small step-size regimes, distributed agents match centralized strategy performance.

Performance is influenced by network topology and operational parameters.

Abstract

Part I of this work examined the mean-square stability and convergence of the learning process of distributed strategies over graphs. The results identified conditions on the network topology, utilities, and data in order to ensure stability; the results also identified three distinct stages in the learning behavior of multi-agent networks related to transient phases I and II and the steady-state phase. This Part II examines the steady-state phase of distributed learning by networked agents. Apart from characterizing the performance of the individual agents, it is shown that the network induces a useful equalization effect across all agents. In this way, the performance of noisier agents is enhanced to the same level as the performance of agents with less noisy data. It is further shown that in the small step-size regime, each agent in the network is able to achieve the same performance level as that of a centralized strategy corresponding to a fully connected network. The results in this part reveal explicitly which aspects of the network topology and operation influence performance and provide important insights into the design of effective mechanisms for the processing and diffusion of information over networks.