Accelerated Stochastic Gradient Method with Applications to Consensus Problem in Markov-Varying Networks

TL;DR

This paper introduces an accelerated stochastic gradient method tailored for Markovian noise scenarios, with applications to consensus problems in dynamic networks, demonstrating improved efficiency and convergence over traditional methods.

Contribution

The paper presents a novel first-order optimization algorithm with Nesterov acceleration for Markovian noise, and applies it to consensus problems in time-varying networks.

Findings

The proposed method outperforms classic approaches in experiments.

Convergence is established under noise depending on the distance to the solution.

Application to consensus problems shows improved agreement among agents.

Abstract

Stochastic optimization is a vital field in the realm of mathematical optimization, finding applications in diverse areas ranging from operations research to machine learning. In this paper, we introduce a novel first-order optimization algorithm designed for scenarios where Markovian noise is present, incorporating Nesterov acceleration for enhanced efficiency. The convergence analysis is performed using an assumption on noise depending on the distance to the solution. We also delve into the consensus problem over Markov-varying networks, exploring how this algorithm can be applied to achieve agreement among multiple agents with differing objectives during changes in the communication system. To show the performance of our method on the problem above, we conduct experiments to demonstrate the superiority over the classic approach.