Achieving Linear Speedup with ProxSkip in Distributed Stochastic Optimization

TL;DR

This paper proves that decentralized ProxSkip achieves linear speedup in distributed stochastic optimization, effectively reducing communication costs across various convexity settings.

Contribution

It provides the first unified convergence analysis showing linear speedup of decentralized ProxSkip under stochastic gradients in non-convex, convex, and strongly convex problems.

Findings

Decentralized ProxSkip achieves linear speedup with respect to the number of nodes.

Local updates reduce communication frequency and improve efficiency.

The analysis accounts for gradient noise, network connectivity, and data heterogeneity.

Abstract

The ProxSkip algorithm for distributed optimization is gaining increasing attention due to its effectiveness in reducing communication. However, existing analyses of ProxSkip are limited to the strongly convex setting and fail to achieve linear speedup with respect to the number of nodes. Key questions regarding its behavior in the non-convex setting and the achievability of linear speedup remain open. In this paper, we revisit decentralized ProxSkip and answer these questions affirmatively. We provide a unified convergence analysis for stochastic non-convex, convex, and strongly convex problems, revealing how gradient noise, local updates, network connectivity, and data heterogeneity jointly determine the convergence behavior. To the best of our knowledge, this is the first analysis showing that decentralized ProxSkip achieves linear speedup in the number of nodes under stochastic gradients. Moreover, our results demonstrate that local updates can effectively reduce communication frequency and improve communication efficiency.