Accelerated Multi-Agent Optimization Method over Stochastic Networks

TL;DR

This paper introduces an accelerated distributed optimization algorithm for multi-agent systems operating over stochastic networks, achieving fast convergence rates for strongly convex problems with practical simulation results.

Contribution

It develops a novel Nesterov-based method for stochastic networked multi-agent optimization with proven convergence rates and demonstrates its effectiveness through simulation.

Findings

Expected dual values converge at a rate of O(1/k^2)

Method works over time-varying stochastic networks

Simulation confirms efficiency in optimal power flow problems

Abstract

We propose a distributed method to solve a multi-agent optimization problem with strongly convex cost function and equality coupling constraints. The method is based on Nesterov's accelerated gradient approach and works over stochastically time-varying communication networks. We consider the standard assumptions of Nesterov's method and show that the sequence of the expected dual values converge toward the optimal value with the rate of $\mathcal{O}(1/k^2)$. Furthermore, we provide a simulation study of solving an optimal power flow problem with a well-known benchmark case.