Diffusion Adaptation Strategies for Distributed Optimization and Learning over Networks

TL;DR

This paper introduces a diffusion-based adaptive algorithm for distributed optimization over networks, enabling real-time cooperation, noise mitigation, and robustness to failures, applicable to dynamic and sparse estimation problems.

Contribution

It presents a novel diffusion adaptation strategy that improves distributed learning by allowing continuous, robust, and adaptive cooperation among network nodes.

Findings

Diffusion algorithms outperform incremental methods in robustness and flexibility.

The method effectively handles sparse parameter estimation and localization tasks.

Performance analysis shows favorable steady-state and transient behavior.

Abstract

We propose an adaptive diffusion mechanism to optimize a global cost function in a distributed manner over a network of nodes. The cost function is assumed to consist of a collection of individual components. Diffusion adaptation allows the nodes to cooperate and diffuse information in real-time; it also helps alleviate the effects of stochastic gradient noise and measurement noise through a continuous learning process. We analyze the mean-square-error performance of the algorithm in some detail, including its transient and steady-state behavior. We also apply the diffusion algorithm to two problems: distributed estimation with sparse parameters and distributed localization. Compared to well-studied incremental methods, diffusion methods do not require the use of a cyclic path over the nodes and are robust to node and link failure. Diffusion methods also endow networks with adaptation abilities that enable the individual nodes to continue learning even when the cost function changes with time. Examples involving such dynamic cost functions with moving targets are common in the context of biological networks.