On the O(1/k) Convergence of Asynchronous Distributed Alternating Direction Method of Multipliers

TL;DR

This paper introduces an asynchronous distributed ADMM algorithm for solving coupled optimization problems across a network of agents, achieving an O(1/k) convergence rate, improving upon previous methods that required synchronization.

Contribution

It presents a novel asynchronous ADMM method for general distributed optimization, demonstrating convergence at an O(1/k) rate without requiring synchronization among agents.

Findings

Achieves O(1/k) convergence rate for asynchronous ADMM.

Removes the need for synchronous implementation and global agent ordering.

Extends applicability to general distributed optimization problems.

Abstract

We consider a network of agents that are cooperatively solving a global optimization problem, where the objective function is the sum of privately known local objective functions of the agents and the decision variables are coupled via linear constraints. Recent literature focused on special cases of this formulation and studied their distributed solution through either subgradient based methods with O(1/sqrt(k)) rate of convergence (where k is the iteration number) or Alternating Direction Method of Multipliers (ADMM) based methods, which require a synchronous implementation and a globally known order on the agents. In this paper, we present a novel asynchronous ADMM based distributed method for the general formulation and show that it converges at the rate O(1/k).