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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2018, Volume 21, Number 1, Pages 47–53
DOI: https://doi.org/10.15372/SJNM20180103
(Mi sjvm667)
 

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

Parallel algorithms and probability of large deviation for stochastic convex optimization problems

P. Dvurechenskyab, A. Gasnikovbc, A. Lagunovskayac

a Weierstrass Institute for Applied Analysis and Stochastics, 39 Mohrenstr., Berlin, 10117, Germany
b Institute for Information Transmission Problems RAS, 19, build. 1, Bolshoy Karetny per., Moscow, 127051, Russia
c Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny, 141700, Russia
Full-text PDF (496 kB) Citations (8)
References:
Abstract: In this paper, convex stochastic optimization problems under different assumptions on the properties of the available stochastic subgradients are considered. It is known that if a value of the objective function is available, one can obtain, in parallel, several independent approximate solutions in terms of the objective residual expectation. Then, choosing a solution with the minimum function value, one can control the probability of large deviations of the objective residual. On the contrary, in this short paper we address the situation when the objective function value is unavailable or is too expensive to calculate. Under the “light-tail” assumption for stochastic subgradients and in the general case with a moderate probability of large deviations, it is shown that parallelization combined with averaging gives bounds for the probability of large deviations similar to those of a serial method. Thus, in these cases one can benefit from parallel computations and reduce the computational time without any loss in the solution quality.
Key words: stochastic convex optimization, probability of large deviation, mirror descent, parallel algorithm.
Funding agency Grant number
Russian Science Foundation 14-50-00150
Ministry of Education and Science of the Russian Federation МК-1806.2017.9
Received: 24.01.2017
Revised: 07.07.2017
English version:
Numerical Analysis and Applications, 2018, Volume 11, Issue 1, Pages 33–37
DOI: https://doi.org/10.1134/S1995423918010044
Bibliographic databases:
Document Type: Article
UDC: 519.856+519.856.3
Language: Russian
Citation: P. Dvurechensky, A. Gasnikov, A. Lagunovskaya, “Parallel algorithms and probability of large deviation for stochastic convex optimization problems”, Sib. Zh. Vychisl. Mat., 21:1 (2018), 47–53; Num. Anal. Appl., 11:1 (2018), 33–37
Citation in format AMSBIB
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