Multitask Diffusion Adaptation over Networks

TL;DR

This paper introduces diffusion-based distributed algorithms for multitask learning over networks, enabling multiple parameter vectors to be estimated collaboratively, with proven stability and convergence, applicable to spectral sensing, localization, and data unmixing.

Contribution

It develops novel multitask diffusion algorithms with stability analysis, extending distributed optimization to multiple simultaneous parameter estimations.

Findings

Algorithms are stable in mean and mean-square sense.

Simulations confirm theoretical stability and effectiveness.

Applicable to spectral sensing, target localization, and hyperspectral data unmixing.

Abstract

Adaptive networks are suitable for decentralized inference tasks, e.g., to monitor complex natural phenomena. Recent research works have intensively studied distributed optimization problems in the case where the nodes have to estimate a single optimum parameter vector collaboratively. However, there are many important applications that are multitask-oriented in the sense that there are multiple optimum parameter vectors to be inferred simultaneously, in a collaborative manner, over the area covered by the network. In this paper, we employ diffusion strategies to develop distributed algorithms that address multitask problems by minimizing an appropriate mean-square error criterion with $\ell_2$-regularization. The stability and convergence of the algorithm in the mean and in the mean-square sense is analyzed. Simulations are conducted to verify the theoretical findings, and to illustrate how the distributed strategy can be used in several useful applications related to spectral sensing, target localization, and hyperspectral data unmixing.