A distributed ADMM-like method for resource sharing over time-varying networks

TL;DR

This paper introduces a distributed primal-dual algorithm for multi-agent resource sharing over dynamic networks, achieving convergence with quantifiable rates and outperforming centralized methods in specific applications.

Contribution

It presents a novel distributed primal-dual algorithm tailored for time-varying networks, with convergence guarantees and performance analysis.

Findings

Convergence rates depend on network topology.

Algorithm effectively solves resource sharing problems.

Outperforms centralized methods in basis pursuit denoising.

Abstract

We consider cooperative multi-agent resource sharing problems over time-varying communication networks, where only local communications are allowed. The objective is to minimize the sum of agent-specific composite convex functions subject to a conic constraint that couples agents' decisions. We propose a distributed primal-dual algorithm DPDA-D to solve the saddle point formulation of the sharing problem on time-varying (un)directed communication networks; and we show that primal-dual iterate sequence converges to a point defined by a primal optimal solution and a consensual dual price for the coupling constraint. Furthermore, we provide convergence rates for suboptimality, infeasibility and consensus violation of agents' dual price assessments; examine the effect of underlying network topology on the convergence rates of the proposed decentralized algorithm; and compare DPDA-D with a centralized method on the basis pursuit denoising and multi-channel power allocation problems.