An Accelerated Method For Decentralized Distributed Stochastic Optimization Over Time-Varying Graphs

TL;DR

This paper introduces the first accelerated decentralized stochastic optimization method that achieves near-optimal communication and oracle complexities, even over time-varying graphs, advancing distributed learning efficiency.

Contribution

It proposes a novel accelerated algorithm for decentralized stochastic optimization that handles time-varying communication graphs with optimal complexity bounds.

Findings

Achieves near-optimal communication complexity bounds.

Attains optimal oracle complexity bounds for smooth strongly convex functions.

First to provide upper complexity bounds for time-varying graphs in this context.

Abstract

We consider a distributed stochastic optimization problem that is solved by a decentralized network of agents with only local communication between neighboring agents. The goal of the whole system is to minimize a global objective function given as a sum of local objectives held by each agent. Each local objective is defined as an expectation of a convex smooth random function and the agent is allowed to sample stochastic gradients for this function. For this setting we propose the first accelerated (in the sense of Nesterov's acceleration) method that simultaneously attains optimal up to a logarithmic factor communication and oracle complexity bounds for smooth strongly convex distributed stochastic optimization. We also consider the case when the communication graph is allowed to vary with time and obtain complexity bounds for our algorithm, which are the first upper complexity bounds for this setting in the literature.