Diffusion LMS over multitask networks

The diffusion LMS algorithm has been extensively studied in recent years. This efficient strategy allows to address distributed optimization problems over networks in the case where nodes have to collaboratively estimate a single parameter vector. Nevertheless, there are several problems in practice that are multitask-oriented in the sense that the optimum parameter vector may not be the same for every node. This brings up the issue of studying the performance of the diffusion LMS algorithm when it is run, either intentionally or unintentionally, in a multitask environment. In this paper, we conduct a theoretical analysis on the stochastic behavior of diffusion LMS in the case where the single-task hypothesis is violated. We analyze the competing factors that influence the performance of diffusion LMS in the multitask environment, and which allow the algorithm to continue to deliver performance superior to non-cooperative strategies in some useful circumstances. We also propose an unsupervised clustering strategy that allows each node to select, via adaptive adjustments of combination weights, the neighboring nodes with which it can collaborate to estimate a common parameter vector. Simulations are presented to illustrate the theoretical results, and to demonstrate the efficiency of the proposed clustering strategy.