Algorithms of Robust Stochastic Optimization Based on Mirror Descent Method

A. V. Nazin; A. S. Nemirovsky; A. B. Tsybakov; A. B. Juditsky

doi:10.1134/S0005117919090042

Algorithms of Robust Stochastic Optimization Based on Mirror Descent Method

A. V. Nazin, A. S. Nemirovsky, A. B. Tsybakov, A. B. Juditsky

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1607-1627
Number of pages	21
Journal	Automation and Remote Control
Volume	80
Issue number	9
DOIs	https://doi.org/10.1134/S0005117919090042
Publication status	Published - 1 Sept 2019
Externally published	Yes

Keywords

convex composite stochastic optimization
mirror descent method
robust confidence sets
robust iterative algorithms
stochastic optimization algorithms

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10.1134/S0005117919090042

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title = "Algorithms of Robust Stochastic Optimization Based on Mirror Descent Method",

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 = "convex composite stochastic optimization, mirror descent method, robust confidence sets, robust iterative algorithms, stochastic optimization algorithms",

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AU - Nazin, A. V.

AU - Nemirovsky, A. S.

AU - Tsybakov, A. B.

AU - Juditsky, A. B.

PY - 2019/9/1

Y1 - 2019/9/1

N2 - 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.

AB - 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.

KW - convex composite stochastic optimization

KW - mirror descent method

KW - robust confidence sets

KW - robust iterative algorithms

KW - stochastic optimization algorithms

U2 - 10.1134/S0005117919090042

DO - 10.1134/S0005117919090042

M3 - Article

AN - SCOPUS:85072963520

SN - 0005-1179

VL - 80

SP - 1607

EP - 1627

JO - Automation and Remote Control

JF - Automation and Remote Control

IS - 9

ER -

Algorithms of Robust Stochastic Optimization Based on Mirror Descent Method

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Keywords

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