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Tighter Theory for Local SGD on Identical and Heterogeneous Data

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arxiv 1909.04746 v4 pith:I3WPCY2T submitted 2019-09-10 cs.LG cs.DCcs.NAmath.NAmath.OCstat.ML

Tighter Theory for Local SGD on Identical and Heterogeneous Data

classification cs.LG cs.DCcs.NAmath.NAmath.OCstat.ML
keywords localdataheterogeneousidenticalnumberoptimaltheoryanalysis
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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