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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2024, Volume 64, Number 4, paper published in the English version journal (Mi zvmmf11740)  

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

Papers published in the English version of the journal

Highly smooth zeroth-order methods for solving optimization problems under the PL condition

A. V. Gasnikovabc, A. V. Lobanovac, F. S. Stonyakinad

a Moscow Institute of Physics and Technology, 141700, Dolgoprudny, Russia
b Innopolis University, 420500, Innopolis, Russia
c Institute for System Programming, Russian Academy of Sciences, 125047, Moscow, Russia
d V.I. Vernadsky Crimean Federal University, 295007, Simferopol, Russia
Citations (8)
Abstract: In this paper, we study the black box optimization problem under the Polyak–Lojasiewicz (PL) condition, assuming that the objective function is not just smooth, but has higher smoothness. By using “kernel-based” approximations instead of the exact gradient in the Stochastic Gradient Descent method, we improve the best-known results of convergence in the class of gradient-free algorithms solving problems under the PL condition. We generalize our results to the case where a zeroth-order oracle returns a function value at a point with some adversarial noise. We verify our theoretical results on the example of solving a system of nonlinear equations.
Key words: black-box optimization, gradient-free methods, kernel approximation, maximum noise level.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FSMG-2024-0011
The research was supported by the Ministry of Science and Higher Education of the Russian Federation (state assignment), project no. FSMG-2024-0011.
Received: 05.11.2023
Accepted: 07.06.2024
English version:
Computational Mathematics and Mathematical Physics, 2024, Volume 64, Issue 4, Pages 739–770
DOI: https://doi.org/10.1134/S0965542524700118
Document Type: Article
Language: English
Citation: A. V. Gasnikov, A. V. Lobanov, F. S. Stonyakin, “Highly smooth zeroth-order methods for solving optimization problems under the PL condition”, Comput. Math. Math. Phys., 64:4 (2024), 739–770
Citation in format AMSBIB
\Bibitem{GasLobSto24}
\by A.~V.~Gasnikov, A.~V.~Lobanov, F.~S.~Stonyakin
\paper Highly smooth zeroth-order methods for solving optimization problems under the PL condition
\jour Comput. Math. Math. Phys.
\yr 2024
\vol 64
\issue 4
\pages 739--770
\mathnet{http://mi.mathnet.ru/zvmmf11740}
\crossref{https://doi.org/10.1134/S0965542524700118}
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  • 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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