Distributed Forward-Backward Methods without Central Coordination

Abstract

In this work, we propose and analyse forward-backward-type algorithms for finding a zero in 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 the need for a central coordinator to enforce consensus between nodes.