Startseite Decentralized and parallel primal and dual accelerated methods for stochastic convex programming problems
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Decentralized and parallel primal and dual accelerated methods for stochastic convex programming problems

  • Darina Dvinskikh EMAIL logo und Alexander Gasnikov
Veröffentlicht/Copyright: 22. Januar 2021

Abstract

We introduce primal and dual stochastic gradient oracle methods for decentralized convex optimization problems. Both for primal and dual oracles, the proposed methods are optimal in terms of the number of communication steps. However, for all classes of the objective, the optimality in terms of the number of oracle calls per node takes place only up to a logarithmic factor and the notion of smoothness. By using mini-batching technique, we show that the proposed methods with stochastic oracle can be additionally parallelized at each node. The considered algorithms can be applied to many data science problems and inverse problems.

MSC 2010: 90C25; 90C06; 90C15

Award Identifier / Grant number: 18-71-10108

Award Identifier / Grant number: 19-31-51001

Award Identifier / Grant number: 075-00337-20-03

Award Identifier / Grant number: 0714-2020-0005

Funding statement: The work of D. Dvinskikh was supported (Sections 1 and 5) by RFBR 19-31-51001 and funded (Section 6) by the Russian Science Foundation (Project 18-71-10108). The work of A. Gasnikov was supported by the Ministry of Science and Higher Education of the Russian Federation (Goszadaniye) No. 075-00337-20-03, Project No. 0714-2020-0005.

Acknowledgements

We would like to thank F. Bach, P. Dvurechensky, E. Gorbunov, A. Koloskova, A. Kulunchakov, J. Mairal, A. Nemirovski, A. Olshevsky, S. Parsegov, B. Polyak, N. Srebro A. Taylor and C. Uribe for useful discussions.

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Received: 2020-11-19
Accepted: 2020-12-10
Published Online: 2021-01-22
Published in Print: 2021-06-01

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