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arXiv · 2505.10889

Convergence Analysis of the Last Iterate in Distributed Stochastic Gradient Descent with Momentum

Difei Cheng·Ruinan Jin·Hong Qiao·Bo Zhang
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Abstract

Distributed stochastic gradient methods are widely used to preserve data privacy and ensure scalability in large-scale learning tasks. While existing theory on distributed momentum Stochastic Gradient Descent (mSGD) mainly focuses on time-averaged convergence, the more practical last-iterate convergence remains underexplored. In this work, we analyze the last-iterate convergence behavior of distributed mSGD in non-convex settings under the classical Robbins-Monro step-size schedule. We prove both almost sure convergence and $L_2$ convergence of the last iterate, and derive convergence rates. We further show that momentum can accelerate early-stage convergence, and provide experiments to support our theory.

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Difei Cheng, Ruinan Jin, Hong Qiao, Bo Zhang. 2025-05-16. Convergence Analysis of the Last Iterate in Distributed Stochastic Gradient Descent with Momentum. https://arxiv.org/abs/2505.10889

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