ACCELERATED STOCHASTIC APPROXIMATION

被引：37

作者：

Delyon, Bernard ^{[1
]}

Juditsky, Anatoli ^{[1
]}

机构：

[1] Inst Natl Rech Informat & Automat, Inst Rech Informat & Syst Aleatoires, F-35042 Rennes, France

来源：

SIAM JOURNAL ON OPTIMIZATION | 1993年 / 3卷 / 04期

关键词：

stochastic approximation; accelerated algorithms; optimal algorithms;

D O I：

10.1137/0803045

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A technique to accelerate convergence of stochastic approximation algorithms is studied. It is based on Kesten's idea of equalization of the gain coefficient for the Robbins-Monro algorithm. Convergence with probability is proved for the multidimensional analog of the Kesten accelerated stochastic approximation algorithm. Asymptotic normality of the delivered estimates is also shown. Results of numerical simulations are presented that demonstrate the efficiency of the acceleration procedure.

引用

页码：868 / 881

页数：14

共 15 条

[1]

[Anonymous], 1973, STOCHASTIC APPROXIMA

[2]

[Anonymous], 1978, STOCHASTIC APPROXIMA

[3]

[Anonymous], 1990, ADAPTIVE ALGORITHMS

[4]

Breiman L., 1968, PROBABILITY

[5] ASYMPTOTICALLY EFFICIENT RECURSIVE ESTIMATION [J].

FABIAN, V .

ANNALS OF STATISTICS, 1978, 6 (04) :854-866

[6] ACCELERATED STOCHASTIC-APPROXIMATION [J].

KESTEN, H .

ANNALS OF MATHEMATICAL STATISTICS, 1958, 29 (01) :41-59

[7]

Neveu J., 1972, MARTINGALES TEMPS DI

[8]

POLYAK B. T., 1991, SIAM J CONTROL OPTIM, V29, P838

[9]

POLYAK B. T., 1980, AUTOMAT REM CONTR+, V40, P378

[10] A STOCHASTIC APPROXIMATION METHOD [J].

ROBBINS, H ;

MONRO, S .

ANNALS OF MATHEMATICAL STATISTICS, 1951, 22 (03) :400-407

← 1 2 →