Distributed Forward-Backward Methods for Ring Networks

TL;DR

This paper introduces distributed forward-backward algorithms for ring networks that enable decentralized computation of monotone operator zeros without requiring global consensus, improving scalability and efficiency.

Contribution

It proposes novel distributed algorithms for monotone operator problems that do not rely on reduction to product spaces, suitable for ring network implementations.

Findings

Algorithms require one resolvent and forward evaluation per iteration.

Suitable for decentralized ring network architectures.

No need for global summation to achieve consensus.

Abstract

In this work, we propose and analyse forward-backward-type algorithms for finding a zero of the sum of finitely many monotone operators, which are not based on reduction to a two operator inclusion in the product space. Each iteration of the studied algorithms requires one resolvent evaluation per set-valued operator, one forward evaluation per cocoercive operator, and two forward evaluations per monotone operator. Unlike existing methods, the structure of the proposed algorithms are suitable for distributed, decentralised implementation in ring networks without needing global summation to enforce consensus between nodes.