Linearly converging error compensated SGD

Eduard Gorbunov, Dmitry Kovalev, Dmitry Makarenko, Peter Richtárik

Research output: Contribution to conferencePaperpeer-review

38 Scopus citations


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.

Original languageEnglish (US)
StatePublished - 2020
Event34th Conference on Neural Information Processing Systems, NeurIPS 2020 - Virtual, Online
Duration: Dec 6 2020Dec 12 2020


Conference34th Conference on Neural Information Processing Systems, NeurIPS 2020
CityVirtual, Online

Bibliographical note

Funding Information:
The work of Peter Richtárik, Eduard Gorbunov and Dmitry Kovalev was supported by KAUST Baseline Research Fund. Part of this work was done while E. Gorbunov was a research intern at KAUST. The work of E. Gorbunov in Sections 4, A–D, H, and K was also partially supported by the Ministry of Science and Higher Education of the Russian Federation (Goszadaniye) 075-00337-20-03, project No. 0714-2020-0005, and in Sections 3, E–G, I, J – by RFBR, project number 19-31-51001.

Publisher Copyright:
© 2020 Neural information processing systems foundation. All rights reserved.

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing


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