A Sparsity-Aware Adaptive Algorithm for Distributed Learning

TL;DR

This paper introduces a sparsity-aware adaptive algorithm for distributed learning in networks, combining set-theoretic estimation with variable metric projections to improve sparse signal recovery.

Contribution

It develops a novel distributed algorithm that incorporates sparsity constraints via hyperslabs and weighted l1 balls, with proven convergence properties.

Findings

The proposed scheme converges monotonically and asymptotically.

Numerical results show improved performance over existing sparse learning algorithms.

The method effectively enforces sparsity while maintaining consensus in the network.

Abstract

In this paper, a sparsity-aware adaptive algorithm for distributed learning in diffusion networks is developed. The algorithm follows the set-theoretic estimation rationale. At each time instance and at each node of the network, a closed convex set, known as property set, is constructed based on the received measurements; this defines the region in which the solution is searched for. In this paper, the property sets take the form of hyperslabs. The goal is to find a point that belongs to the intersection of these hyperslabs. To this end, sparsity encouraging variable metric projections onto the hyperslabs have been adopted. Moreover, sparsity is also imposed by employing variable metric projections onto weighted $\ell_1$ balls. A combine adapt cooperation strategy is adopted. Under some mild assumptions, the scheme enjoys monotonicity, asymptotic optimality and strong convergence to a point that lies in the consensus subspace. Finally, numerical examples verify the validity of the proposed scheme, compared to other algorithms, which have been developed in the context of sparse adaptive learning.