Distributed Mirror Descent with Integral Feedback: Asymptotic Convergence Analysis of Continuous-time Dynamics

TL;DR

This paper introduces a continuous-time distributed mirror descent algorithm with integral feedback, enabling convergence to the global optimum using only local information, and demonstrates its effectiveness through theoretical analysis and numerical experiments.

Contribution

It presents a novel distributed mirror descent method with integral feedback that guarantees asymptotic convergence with a constant step-size.

Findings

The algorithm converges asymptotically to the global optimum.

Integral feedback improves the convergence rate.

Numerical experiments verify the theoretical advantages.

Abstract

This work addresses distributed optimization, where a network of agents wants to minimize a global strongly convex objective function. The global function can be written as a sum of local convex functions, each of which is associated with an agent. We propose a continuous-time distributed mirror descent algorithm that uses purely local information to converge to the global optimum. Unlike previous work on distributed mirror descent, we incorporate an integral feedback in the update, allowing the algorithm to converge with a constant step-size when discretized. We establish the asymptotic convergence of the algorithm using Lyapunov stability analysis. We further illustrate numerical experiments that verify the advantage of adopting integral feedback for improving the convergence rate of distributed mirror descent.