# A Multitask Diffusion Strategy with Optimized Inter-Cluster Cooperation

## TL;DR

This paper introduces a multitask diffusion strategy for networked nodes performing separate least-mean-squares estimations, ensuring stability and unbiasedness, with a novel local weight optimization scheme that improves steady-state performance.

## Contribution

It proposes a new multitask diffusion algorithm with guaranteed stability and unbiasedness, plus a local weight selection method for enhanced network performance.

## Key findings

- Lower steady-state mean-square deviation compared to existing methods
- Ensures mean stability regardless of inter-cluster weights
- Achieves asymptotically unbiased estimation when parameters share the same mean

## Abstract

We consider a multitask estimation problem where nodes in a network are divided into several connected clusters, with each cluster performing a least-mean-squares estimation of a different random parameter vector. Inspired by the adapt-then-combine diffusion strategy, we propose a multitask diffusion strategy whose mean stability can be ensured whenever individual nodes are stable in the mean, regardless of the inter-cluster cooperation weights. In addition, the proposed strategy is able to achieve an asymptotically unbiased estimation, when the parameters have same mean. We also develop an inter-cluster cooperation weights selection scheme that allows each node in the network to locally optimize its inter-cluster cooperation weights. Numerical results demonstrate that our approach leads to a lower average steady-state network mean-square deviation, compared with using weights selected by various other commonly adopted methods in the literature.