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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2023, Volume 63, Number 9, Pages 1458–1512
DOI: https://doi.org/10.31857/S0044466923090028
(Mi zvmmf11614)
 

This article is cited in 8 scientific papers (total in 8 papers)

Optimal control

Gradient-free federated learning methods with $l_1$ and $l_2$-randomization for non-smooth convex stochastic optimization problems

B. A. Alashkara, A. V. Gasnikovabc, D. M. Dvinskikhd, A. V. Lobanovaef

a Moscow Institute of Physics and Technology, Dolgoprudny, Russia
b Institute for Information Transmission Problems RAS, Moscow, Russia
c Caucasus Mathematical Center, Adyghe State University, Maikop, Russia
d National Research University Higher School of Economics, Moscow, Russia
e ISP RAS Research Center for Trusted Artificial Intelligence, Moscow, Russia
f Moscow Aviation Institute, Moscow, Russia
Citations (8)
Abstract: This paper studies non-smooth problems of convex stochastic optimization. Using the smoothing technique based on the replacement of the function value at the considered point by the averaged function value over a ball (in $l_1$-norm or $l_2$-norm) of a small radius centered at this point, and then the original problem is reduced to a smooth problem (whose Lipschitz constant of the gradient is inversely proportional to the radius of the ball). An essential property of the smoothing used is the possibility of calculating an unbiased estimation of the gradient of a smoothed function based only on realizations of the original function. The obtained smooth stochastic optimization problem is proposed to be solved in a distributed federated learning architecture (the problem is solved in parallel: nodes make local steps, e.g. stochastic gradient descent, then communicate–all with all, then all this is repeated). The goal of the article is to build on the basis of modern achievements in the field of gradient–free non-smooth optimization and in the field of federated learning gradient-free methods for solving problems of non-smooth stochastic optimization in the architecture of federated learning.
Key words: gradient-free methods, inexact oracle, federated learning.
Funding agency Grant number
Russian Science Foundation 23-11-00229
The research was supported by the Russian Science Foundation (project no. 23-11-00229), https://rscf.ru/en/project/23-11-00229/.
Received: 18.11.2022
Revised: 20.05.2023
Accepted: 29.05.2023
English version:
Computational Mathematics and Mathematical Physics, 2023, Volume 63, Issue 9, Pages 1600–1653
DOI: https://doi.org/10.1134/S0965542523090026
Bibliographic databases:
Document Type: Article
UDC: 519.85
Language: Russian
Citation: B. A. Alashkar, A. V. Gasnikov, D. M. Dvinskikh, A. V. Lobanov, “Gradient-free federated learning methods with $l_1$ and $l_2$-randomization for non-smooth convex stochastic optimization problems”, Zh. Vychisl. Mat. Mat. Fiz., 63:9 (2023), 1458–1512; Comput. Math. Math. Phys., 63:9 (2023), 1600–1653
Citation in format AMSBIB
\Bibitem{AlaGasDvi23}
\by B.~A.~Alashkar, A.~V.~Gasnikov, D.~M.~Dvinskikh, A.~V.~Lobanov
\paper Gradient-free federated learning methods with $l_1$ and $l_2$-randomization for non-smooth convex stochastic optimization problems
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2023
\vol 63
\issue 9
\pages 1458--1512
\mathnet{http://mi.mathnet.ru/zvmmf11614}
\crossref{https://doi.org/10.31857/S0044466923090028}
\elib{https://elibrary.ru/item.asp?id=54313682}
\transl
\jour Comput. Math. Math. Phys.
\yr 2023
\vol 63
\issue 9
\pages 1600--1653
\crossref{https://doi.org/10.1134/S0965542523090026}
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  • https://www.mathnet.ru/eng/zvmmf/v63/i9/p1458
  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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