Diffusion Adaptation Strategies for Distributed Optimization and Learning over Networks

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.Comment: 34 pages, 6 figures, to appear in IEEE Transactions on Signal Processing, 201

Performance of diffusion adaptation for collaborative optimization

We derive an adaptive diffusion mechanism to optimize global cost functions in a distributed manner over a network of nodes. The cost function is assumed to consist of the sum of individual components, and diffusion adaptation is used to enable the nodes to cooperate locally through in-network processing in order to solve the desired optimization problem. We analyze the mean-square-error performance of the algorithm, including its transient and steady-state behavior. We illustrate one application in the context of least-mean-squares estimation for sparse vectors