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dc.contributor.authorGorbunov, Eduard
dc.contributor.authorKovalev, Dmitry
dc.contributor.authorMakarenko, Dmitry
dc.contributor.authorRichtarik, Peter
dc.date.accessioned2020-11-18T13:36:54Z
dc.date.available2020-11-18T13:36:54Z
dc.date.issued2020-10-23
dc.identifier.urihttp://hdl.handle.net/10754/666025
dc.description.abstractIn 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.
dc.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/2010.12292
dc.rightsArchived with thanks to arXiv
dc.titleLinearly Converging Error Compensated SGD
dc.typePreprint
dc.contributor.departmentComputer Science
dc.contributor.departmentComputer Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.eprint.versionPre-print
dc.contributor.institutionMIPT, Russia.
dc.contributor.institutionYandex , Russia.
dc.contributor.institutionSirius, Russia.
dc.identifier.arxivid2010.12292
kaust.personGorbunov, Eduard
kaust.personKovalev, Dmitry
kaust.personRichtarik, Peter
refterms.dateFOA2020-11-18T13:37:50Z


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