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    Linearly Converging Error Compensated SGD

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    Type
    Preprint
    Authors
    Gorbunov, Eduard
    Kovalev, Dmitry cc
    Makarenko, Dmitry
    Richtarik, Peter cc
    KAUST Department
    Computer Science
    Computer Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2020-10-23
    Permanent link to this record
    http://hdl.handle.net/10754/666025
    
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    Abstract
    In this paper, we propose a unified analysis of variants of distributed SGD with arbitrary compressions and delayed updates. Our framework is general enough to cover different variants of quantized SGD, Error-Compensated SGD (EC-SGD) and SGD with delayed updates (D-SGD). Via a single theorem, we derive the complexity results for all the methods that fit our framework. For the existing methods, this theorem gives the best-known complexity results. Moreover, using our general scheme, we develop new variants of SGD that combine variance reduction or arbitrary sampling with error feedback and quantization and derive the convergence rates for these methods beating the state-of-the-art results. In order to illustrate the strength of our framework, we develop 16 new methods that fit this. In particular, we propose the first method called EC-SGD-DIANA that is based on error-feedback for biased compression operator and quantization of gradient differences and prove the convergence guarantees showing that EC-SGD-DIANA converges to the exact optimum asymptotically in expectation with constant learning rate for both convex and strongly convex objectives when workers compute full gradients of their loss functions. Moreover, for the case when the loss function of the worker has the form of finite sum, we modified the method and got a new one called EC-LSVRG-DIANA which is the first distributed stochastic method with error feedback and variance reduction that converges to the exact optimum asymptotically in expectation with a constant learning rate.
    Publisher
    arXiv
    arXiv
    2010.12292
    Additional Links
    https://arxiv.org/pdf/2010.12292
    Collections
    Preprints; Computer Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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