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    Stochastic Distributed Learning with Gradient Quantization and Variance Reduction

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    1904.05115.pdf
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    1.090Mb
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    Description:
    Preprint
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    Type
    Preprint
    Authors
    Horvath, Samuel
    Kovalev, Dmitry
    Mishchenko, Konstantin
    Stich, Sebastian
    Richtarik, Peter cc
    KAUST Department
    Computer Science
    Computer Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Statistics
    Statistics Program
    Date
    2019-04-10
    Permanent link to this record
    http://hdl.handle.net/10754/653103
    
    Metadata
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    Abstract
    We consider distributed optimization where the objective function is spreadamong different devices, each sending incremental model updates to a centralserver. To alleviate the communication bottleneck, recent work proposed variousschemes to compress (e.g.\ quantize or sparsify) the gradients, therebyintroducing additional variance $\omega \geq 1$ that might slow downconvergence. For strongly convex functions with condition number $\kappa$distributed among $n$ machines, we (i) give a scheme that converges in$\mathcal{O}((\kappa + \kappa \frac{\omega}{n} + \omega)$ $\log (1/\epsilon))$steps to a neighborhood of the optimal solution. For objective functions with afinite-sum structure, each worker having less than $m$ components, we (ii)present novel variance reduced schemes that converge in $\mathcal{O}((\kappa +\kappa \frac{\omega}{n} + \omega + m)\log(1/\epsilon))$ steps to arbitraryaccuracy $\epsilon > 0$. These are the first methods that achieve linearconvergence for arbitrary quantized updates. We also (iii) give analysis forthe weakly convex and non-convex cases and (iv) verify in experiments that ournovel variance reduced schemes are more efficient than the baselines.
    Sponsors
    The authors would like to thank Xun Qian for the careful checking of the proofs and for spotting several typos in the analysis.
    Publisher
    arXiv
    arXiv
    1904.05115
    Additional Links
    https://arxiv.org/abs/1904.05115
    https://arxiv.org/pdf/1904.05115
    Collections
    Preprints; Computer Science Program; Statistics Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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