Diffusion Strategies Outperform Consensus Strategies for Distributed Estimation Over Adaptive Networks

TLDR

Adaptive networks consist of nodes with adaptation and learning abilities that interact locally and diffuse information to solve estimation and inference tasks in a distributed manner. This work compares the mean‑square performance of consensus and diffusion strategies for distributed estimation over networks. The study analyzes the two strategies under constant step‑sizes, examining how information diffuses through the network. Diffusion strategies converge faster, achieve lower mean‑square deviation, and maintain stability regardless of combination weights, whereas consensus networks can become unstable and cause catastrophic failure, as confirmed by theory and simulations.

Abstract

Adaptive networks consist of a collection of nodes with adaptation and learning abilities. The nodes interact with each other on a local level and diffuse information across the network to solve estimation and inference tasks in a distributed manner. In this work, we compare the mean-square performance of two main strategies for distributed estimation over networks: consensus strategies and diffusion strategies. The analysis in the paper confirms that under constant step-sizes, diffusion strategies allow information to diffuse more thoroughly through the network and this property has a favorable effect on the evolution of the network: diffusion networks are shown to converge faster and reach lower mean-square deviation than consensus networks, and their mean-square stability is insensitive to the choice of the combination weights. In contrast, and surprisingly, it is shown that consensus networks can become unstable even if all the individual nodes are stable and able to solve the estimation task on their own. When this occurs, cooperation over the network leads to a catastrophic failure of the estimation task. This phenomenon does not occur for diffusion networks: we show that stability of the individual nodes always ensures stability of the diffusion network irrespective of the combination topology. Simulation results support the theoretical findings.