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arXiv · 2409.13155

Convergence of Distributed Adaptive Optimization with Local Updates

Ziheng Cheng·Margalit Glasgow
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Abstract

We study distributed adaptive algorithms with local updates (intermittent communication). Despite the great empirical success of adaptive methods in distributed training of modern machine learning models, the theoretical benefits of local updates within adaptive methods, particularly in terms of reducing communication complexity, have not been fully understood yet. In this paper, for the first time, we prove that \em Local SGD \em with momentum (\em Local \em SGDM) and \em Local \em Adam can outperform their minibatch counterparts in convex and weakly convex settings in certain regimes, respectively. Our analysis relies on a novel technique to prove contraction during local iterations, which is a crucial yet challenging step to show the advantages of local updates, under generalized smoothness assumption and gradient clipping strategy.

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Ziheng Cheng, Margalit Glasgow. 2024-09-20. Convergence of Distributed Adaptive Optimization with Local Updates. https://arxiv.org/abs/2409.13155

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