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    Better Communication Complexity for Local SGD

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    Preprintfile1.pdf
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    Type
    Preprint
    Authors
    Khaled, Ahmed
    Mishchenko, Konstantin
    Richtarik, Peter cc
    KAUST Department
    Computer Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2019-09-10
    Permanent link to this record
    http://hdl.handle.net/10754/660289
    
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    Abstract
    We revisit the local Stochastic Gradient Descent (local SGD) method and prove new convergence rates. We close the gap in the theory by showing that it works under unbounded gradients and extend its convergence to weakly convex functions. Furthermore, by changing the assumptions, we manage to get new bounds that explain in what regimes local SGD is faster that its non-local version. For instance, if the objective is strongly convex, we show that, up to constants, it is sufficient to synchronize $M$ times in total, where $M$ is the number of nodes. This improves upon the known requirement of Stich (2018) of $\sqrt{TM}$ synchronization times in total, where $T$ is the total number of iterations, which helps to explain the empirical success of local SGD.
    Publisher
    arXiv
    arXiv
    1909.04746
    Additional Links
    https://arxiv.org/pdf/1909.04746
    Collections
    Preprints; Computer Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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