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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2023, Volume 514, Number 2, Pages 212–224
DOI: https://doi.org/10.31857/S2686954323601598 (Mi danma466) 		 
SPECIAL ISSUE: ARTIFICIAL INTELLIGENCE AND MACHINE LEARNING TECHNOLOGIES

Optimal analysis of method with batching for monotone stochastic finite-sum variational inequalities

A. Pichugina, M. Pechina, A. Beznosikova, A. Savchenkob, A. Gasnikova

a Moscow Institute of Physics and Technology, Dolgoprudny, Russian Federation
b Sber AI Lab, Moscow, Russian Federation
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DOI: https://doi.org/10.31857/S2686954323601598
Abstract: Variational inequalities are a universal optimization paradigm that is interesting in itself, but also incorporates classical minimization and saddle point problems. Modern realities encourage to consider stochastic formulations of optimization problems. In this paper, we present an analysis of a method that gives optimal convergence estimates for monotone stochastic finite-sum variational inequalities. In contrast to the previous works, our method supports batching and does not lose the oracle complexity optimality. The effectiveness of the algorithm, especially in the case of small but not single batches is confirmed experimentally.
Keywords: stochastic optimization, variational inequalities, finite-sum problems, batching.
Funding agency Grant number
Правительство Российской Федерации 70-2021-00138
The work of A. Pichugin and M. Pechin was supported by a grant for research centers in the field of artificial intelligence, provided by the Analytical Center for the Government of the Russian Federation in accordance with the subsidy agreement (agreement identifier 000000D730321P5Q0002) and the agreement with the Moscow Institute of Physics and Technology dated November 1, 2021 no. 70-2021-00138.
Presented: A. A. Shananin
Received: 01.09.2023
Revised: 15.09.2023
Accepted: 18.10.2023
English version:
Doklady Mathematics, 2023, Volume 108, Issue suppl. 2, Pages S348–S359
DOI: https://doi.org/10.1134/S1064562423701582
Bibliographic databases:
Document Type: Article
UDC: 004.8
Language: Russian
Citation: A. Pichugin, M. Pechin, A. Beznosikov, A. Savchenko, A. Gasnikov, “Optimal analysis of method with batching for monotone stochastic finite-sum variational inequalities”, Dokl. RAN. Math. Inf. Proc. Upr., 514:2 (2023), 212–224; Dokl. Math., 108:suppl. 2 (2023), S348–S359
Citation in format AMSBIB
\Bibitem{PicPecBez23}
\by A.~Pichugin, M.~Pechin, A.~Beznosikov, A.~Savchenko, A.~Gasnikov
\paper Optimal analysis of method with batching for monotone stochastic finite-sum variational inequalities
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2023
\vol 514
\issue 2
\pages 212--224
\mathnet{http://mi.mathnet.ru/danma466}
\crossref{https://doi.org/10.31857/S2686954323601598}
\elib{https://elibrary.ru/item.asp?id=56717818}
\transl
\jour Dokl. Math.
\yr 2023
\vol 108
\issue suppl. 2
\pages S348--S359
\crossref{https://doi.org/10.1134/S1064562423701582}
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