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Avtomatika i Telemekhanika, 2019, Issue 9, Pages 64–90
DOI: https://doi.org/10.1134/S000523101909006X (Mi at15342) 		 
This article is cited in 16 scientific papers (total in 16 papers)

Algorithms of robust stochastic optimization based on mirror descent method

A. V. Nazina, A. S. Nemirovskyb, A. B. Tsybakovc, A. B. Juditskyd

a Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia
b Georgia Institute of Technology, Atlanta, USA
c CREST, ENSAE, Paris, France
d Université Grenoble Alpes, Grenoble, France
Full-text PDF (718 kB) Citations (16)
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DOI: https://doi.org/10.1134/S000523101909006X
Abstract: We propose an approach to the construction of robust non-Euclidean iterative algorithms by convex composite stochastic optimization based on truncation of stochastic gradients. For such algorithms, we establish sub-Gaussian confidence bounds under weak assumptions about the tails of the noise distribution in convex and strongly convex settings. Robust estimates of the accuracy of general stochastic algorithms are also proposed.
Keywords: robust iterative algorithms, stochastic optimization algorithms, convex composite stochastic optimization, mirror descent method, robust confidence sets.
Funding agency Grant number
National Science Foundation CCF-1523768
Russian Science Foundation 16-11-10015
Agence Nationale de la Recherche ANR-11-LABEX-0047
Fondation Mathématique Jacques Hadamard PGMO 2016-2032H
The work of A.V. Nazin was supported by the Russian Science Foundation, project no. 16-11-10015. The work of A.B. Tsybakov was supported by the GENES Institute and by the grant Labex Ecodec (ANR-11-LABEX-0047). The work of A.B. Juditsky was supported by the grant PGMO 2016-2032H and the joint work of A.B. Juditsky with A.S. Nemirovsky was supported by the NSF grant CCF-1523768.

Received: 18.07.2018
Revised: 03.09.2018
Accepted: 08.11.2018
English version:
Automation and Remote Control, 2019, Volume 80, Issue 9, Pages 1607–1627
DOI: https://doi.org/10.1134/S0005117919090042
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. V. Nazin, A. S. Nemirovsky, A. B. Tsybakov, A. B. Juditsky, “Algorithms of robust stochastic optimization based on mirror descent method”, Avtomat. i Telemekh., 2019, no. 9, 64–90; Autom. Remote Control, 80:9 (2019), 1607–1627
Citation in format AMSBIB
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\paper Algorithms of robust stochastic optimization based on mirror descent method
\jour Avtomat. i Telemekh.
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\pages 64--90
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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