An Asynchronous Decentralised Optimisation Algorithm for Nonconvex Problems

TL;DR

This paper introduces a novel asynchronous decentralized optimization algorithm for nonconvex problems, enabling distributed agents to find stationary solutions efficiently with proven convergence.

Contribution

It presents the first decentralized asynchronous algorithm with convergence proof for nonconvex optimization, based on a randomized block coordinate Douglas-Rachford splitting method.

Findings

Demonstrates efficiency on distributed Phase Retrieval.

Shows effectiveness on sparse Principal Component Analysis.

Provides convergence proof for the proposed algorithm.

Abstract

In this paper, we consider nonconvex decentralised optimisation and learning over a network of distributed agents. We develop an ADMM algorithm based on the Randomised Block Coordinate Douglas-Rachford splitting method which enables agents in the network to distributedly and asynchronously compute a set of first-order stationary solutions of the problem. To the best of our knowledge, this is the first decentralised and asynchronous algorithm for solving nonconvex optimisation problems with convergence proof. The numerical examples demonstrate the efficiency of the proposed algorithm for distributed Phase Retrieval and sparse Principal Component Analysis problems.