Diffusion Adaptation Strategies for Distributed Optimization and Learning over Networks

Details Diffusion Adaptation Strategies for Distributed Optimization and Learning over Networks Diffusion Adaptation Strategies for Distributed Optimization and Learning over Networks

2011-10-31

arxiv.org/abs/1111.0034v2

Mathematics

Optimization and Control

34 pages, 6 figures, submitted for publication

Scientific paper

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, and diffusion adaptation allows the nodes to cooperate and diffuse information in real-time and to alleviate the effects of instantaneous approximation 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 algorithms to two application problems: distributed estimation problem with sparse data and collaborative 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 powerful adaptation abilities that enable the individual nodes to continue learning even when the cost function changes with time. Examples involving dynamic cost functions are common in the context of biological networks.

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