A First-Order Algorithm for Decentralised Min-Max Problems

TL;DR

This paper introduces a decentralized first-order algorithm for solving convex-concave min-max problems across a network of agents, combining existing methods to ensure convergence with standard assumptions.

Contribution

It presents a novel decentralized algorithm that merges PG-EXTRA and the forward reflected backward method for min-max problems, enabling distributed optimization.

Findings

Algorithm converges under standard assumptions with non-decaying stepsize.

Effective for connected networks of multiple agents.

Combines techniques from minimization and min-max problem solving.

Abstract

In this work, we consider a connected network of finitely many agents working cooperatively to solve a min-max problem with convex-concave structure. We propose a decentralised first-order algorithm which can be viewed as a non-trivial combination of two algorithms: PG-EXTRA for decentralised minimisation problems and the forward reflected backward method for (non-distributed) min-max problems. In each iteration of our algorithm, each agent computes the gradient of the smooth component of its local objective function as well as the proximal operator of its nonsmooth component, following by a round of communication with its neighbours. Our analysis shows that the sequence generated by the method converges under standard assumptions with non-decaying stepsize.