Distributed Maximum Likelihood using Dynamic Average Consensus

TL;DR

This paper introduces a distributed maximum likelihood algorithm that combines static and dynamic average consensus techniques to achieve performance comparable to centralized methods, with proven exponential convergence.

Contribution

It proposes a novel distributed maximum likelihood algorithm leveraging consensus algorithms, extending first-order methods to distributed settings with exponential convergence guarantees.

Findings

Algorithm achieves exponential convergence to centralized performance

Numerical simulations validate theoretical guarantees

Framework can be extended to higher-order optimization methods

Abstract

This paper presents the formulation and analysis of a novel distributed maximum likelihood algorithm that utilizes a first-order optimization scheme. The proposed approach utilizes a static average consensus algorithm to reach agreement on the initial condition to the iterative optimization scheme and a dynamic average consensus algorithm to reach agreement on the gradient direction. The current distributed algorithm is guaranteed to exponentially recover the performance of the centralized algorithm. Though the current formulation focuses on maximum likelihood algorithm built on first-order methods, it can be easily extended to higher order methods. Numerical simulations validate the theoretical contributions of the paper.