Locally Convex Sparse Learning over Networks

TL;DR

This paper introduces a distributed sparse learning algorithm over networks that reduces communication and processing time by using local convex optimization with $$-norm minimization, and demonstrates its effectiveness through theoretical analysis and simulations.

Contribution

It proposes a novel distributed $$-norm minimization algorithm for sparse signal estimation that converges efficiently with limited communication.

Findings

Converges to the true sparse signal under certain conditions.

Achieves faster convergence compared to global LASSO algorithms.

Shows competitive estimation accuracy in simulations.

Abstract

We consider a distributed learning setup where a sparse signal is estimated over a network. Our main interest is to save communication resource for information exchange over the network and reduce processing time. Each node of the network uses a convex optimization based algorithm that provides a locally optimum solution for that node. The nodes exchange their signal estimates over the network in order to refine their local estimates. At a node, the optimization algorithm is based on an $\ell_1$-norm minimization with appropriate modifications to promote sparsity as well as to include influence of estimates from neighboring nodes. Our expectation is that local estimates in each node improve fast and converge, resulting in a limited demand for communication of estimates between nodes and reducing the processing time. We provide restricted-isometry-property (RIP)-based theoretical analysis on estimation quality. In the scenario of clean observation, it is shown that the local estimates converge to the exact sparse signal under certain technical conditions. Simulation results show that the proposed algorithms show competitive performance compared to a globally optimum distributed LASSO algorithm in the sense of convergence speed and estimation error.