Asynchronous Distributed Optimization using a Randomized Alternating Direction Method of Multipliers

TL;DR

This paper introduces a novel asynchronous distributed optimization method based on randomized ADMM and Douglas-Rachford iterations, enabling networked agents to reach consensus on a shared minimizer despite uncoordinated activations.

Contribution

It extends the classical ADMM to an asynchronous setting using randomized Gauss-Seidel iterations, providing convergence guarantees under mild conditions.

Findings

Convergence to the optimal solution is proven under mild connectivity assumptions.

Numerical experiments validate the effectiveness of the proposed asynchronous method.

The method generalizes existing ADMM algorithms to asynchronous network settings.

Abstract

Consider a set of networked agents endowed with private cost functions and seeking to find a consensus on the minimizer of the aggregate cost. A new class of random asynchronous distributed optimization methods is introduced. The methods generalize the standard Alternating Direction Method of Multipliers (ADMM) to an asynchronous setting where isolated components of the network are activated in an uncoordinated fashion. The algorithms rely on the introduction of randomized Gauss-Seidel iterations of a Douglas-Rachford operator for finding zeros of a sum of two monotone operators. Convergence to the sought minimizers is provided under mild connectivity conditions. Numerical results sustain our claims.