Non-asymptotic error bounds for constant stepsize stochastic approximation for tracking mobile agents

被引：2

作者：

Kumar, Bhumesh ^{[1
,2
]}

Borkar, Vivek ^{[1
]}

Shetty, Akhil ^{[1
,3
]}

机构：

[1] Indian Inst Technol, Dept Elect Engn, Mumbai 400076, Maharashtra, India

[2] Univ Wisconsin, Dept Elect & Comp Engn, 1415 Johnson Dr, Madison, WI 53706 USA

[3] Univ Calif Berkeley, Dept Elect Engn & Comp Sci, Cory Hall,Hearst Ave, Berkeley, CA 94720 USA

来源：

MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS | 2019年 / 31卷 / 04期

关键词：

Stochastic approximation; Constant stepsize; Non-asymptotic bound; Alekseev's formula; Martingale concentration inequalities; Perturbation analysis; Non-stationary optimization; EXPONENTIAL STABILITY; ASYMPTOTIC ANALYSIS; ALGORITHMS; SYSTEMS; CONVERGENCE; SIZE;

D O I：

10.1007/s00498-019-00249-4

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This work revisits the constant stepsize stochastic approximation algorithm for tracking a slowly moving target and obtains a bound for the tracking error that is valid for the entire time axis, using the Alekseev nonlinear variation of constants formula. It is the first non-asymptotic bound for the entire time axis in the sense that it is not based on the vanishing stepsize limit and associated limit theorems unlike prior works, and captures clearly the dependence on problem parameters and the dimension.

引用

页码：589 / 614

页数：26

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