Performance analysis of diffusion LMS in multitask networks

Diffusion LMS algorithm has been extensively studied during the last few years. This efficient approach allows to address distributed optimization problems over sensor networks in the case where the nodes have to collaboratively estimate a single parameter vector. Nevertheless, real-life problems are often multitask-oriented in the sense that the optimum parameter vector may not be the same for every node. In this paper, we conduct a theoretical analysis on the stochastic behavior of diffusion LMS when, either intentionally or unintentionally, applied to multitask problems, that is, in a situation where the founding hypothesis of this algorithm is violated. Simulation results validate our theoretical model. Theoretical analysis and simulation show that collaboration can be still beneficial, and depends on antagonistic effects of the estimation bias-variance trade-off. This work provides a theoretical justification for the need to derive new cooperative algorithms specifically dedicated to multitask problems.