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

Adaptation Algorithm and Theory Based on Generalized Discrepancy

We present a new algorithm for domain adaptation improving upon a discrepancy minimization algorithm previously shown to outperform a number of algorithms for this task. Unlike many previous algorithms for domain adaptation, our algorithm does not consist of a fixed reweighting of the losses over the training sample. We show that our algorithm benefits from a solid theoretical foundation and more favorable learning bounds than discrepancy minimization. We present a detailed description of our algorithm and give several efficient solutions for solving its optimization problem. We also report the results of several experiments showing that it outperforms discrepancy minimization