Diffusion Adaptation Strategies for Distributed Optimization and Learning Over Networks

TLDR

The cost function is composed of individual components, and dynamic cost functions with moving targets are common in biological networks. The study proposes an adaptive diffusion mechanism to optimize a global cost function in a distributed network of nodes. The adaptive diffusion mechanism enables real‑time cooperation among nodes, mitigates stochastic and measurement noise, and its mean‑square‑error performance is analyzed for transient and steady‑state behavior while being applied to distributed estimation with sparse parameters and localization. Diffusion methods outperform incremental methods by eliminating the need for a cyclic path, providing robustness to node and link failures, and allowing continuous learning when the cost function changes over time.

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.