Tighter Theory for Local SGD on Identical and Heterogeneous Data

Ahmed Khaled; Konstantin Mishchenko; Peter Richtárik

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arXiv · 1909.04746

Tighter Theory for Local SGD on Identical and Heterogeneous Data

Ahmed Khaled·Konstantin Mishchenko·Peter Richtárik

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Abstract

We provide a new analysis of local SGD, removing unnecessary assumptions and elaborating on the difference between two data regimes: identical and heterogeneous. In both cases, we improve the existing theory and provide values of the optimal stepsize and optimal number of local iterations. Our bounds are based on a new notion of variance that is specific to local SGD methods with different data. The tightness of our results is guaranteed by recovering known statements when we plug $H=1$, where $H$ is the number of local steps. The empirical evidence further validates the severe impact of data heterogeneity on the performance of local SGD.

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BibTeX RIS

Ahmed Khaled, Konstantin Mishchenko, Peter Richtárik. 2019-09-10. Tighter Theory for Local SGD on Identical and Heterogeneous Data. https://arxiv.org/abs/1909.04746

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