Algorithms of Robust Stochastic Optimization Based on Mirror Descent Method

被引：21

作者：

Nazin, A., V ^{[1
]}

Nemirovsky, A. S. ^{[2
]}

Tsybakov, A. B. ^{[3
]}

Juditsky, A. B. ^{[4
]}

机构：

[1] Russian Acad Sci, Trapeznikov Inst Control Sci, Moscow, Russia

[2] Georgia Inst Technol, Atlanta, GA 30332 USA

[3] ENSAE, CREST, Palaiseau, France

[4] Univ Grenoble Alpes, Grenoble, France

来源：

AUTOMATION AND REMOTE CONTROL | 2019年 / 80卷 / 09期

基金：

俄罗斯科学基金会;

关键词：

robust iterative algorithms; stochastic optimization algorithms; convex composite stochastic optimization; mirror descent method; robust confidence sets; APPROXIMATION ALGORITHMS; CONVERGENCE;

D O I：

10.1134/S0005117919090042

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

页码：1607 / 1627

页数：21

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