Exponentially Converging Distributed Gradient Descent with Intermittent Communication via Hybrid Methods

TL;DR

This paper introduces a hybrid systems approach for multi-agent optimization that combines continuous computation with discrete communication, achieving exponential convergence to the objective's minimizer.

Contribution

It develops a hybrid parallel coordinate descent algorithm with a sample-and-hold strategy, proving exponential convergence under smoothness and strong convexity assumptions.

Findings

System converges exponentially to the minimizer.

Simulation confirms the theoretical convergence rate.

Hybrid approach effectively balances computation and communication.

Abstract

We present a hybrid systems framework for multi-agent optimization in which agents execute computations in continuous time and communicate in discrete time. The optimization algorithm is a hybrid version of parallelized coordinate descent. Agents implement a sample-and-hold strategy in which gradients are computed at communication times and held constant during flows between communications. Completeness of maximal solutions under these hybrid dynamics is established. Under assumptions of smoothness and strong convexity, we show that this system exponentially converges to the minimizer of an objective function. Simulation results illustrate this convergence rate.