Asymptotic efficiency of perturbation-analysis-based stochastic approximation with averaging

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	Asymptotic efficiency of perturbation-analysis-based stochastic approximation with averaging
	Tang, QY ; L'Ecuyer, P ; Chen, HF
	1999
发表期刊	SIAM JOURNAL ON CONTROL AND OPTIMIZATION
ISSN	0363-0129
卷号	37 期号:6 页码:1822-1847
摘要	Central limit theorems are obtained for the perturbation analysis Robbins-Monro single run (PARMSR) algorithm updated either after every regenerative cycle or after every fixed-length observation period, and with averaging of the iterates, for one-dependent regenerative processes. When the convergence to the optimizer is expressed in terms of the total observation time of the system (or the total computing budget in the case of a simulation), the convergence rate and the limit covariance matrix turn out to be the same for all updating schemes and are optimal within the class of stochastic approximation-algorithms under certain assumptions. A bound on the strong convergence rate of the usual PARMSR algorithm updated after every fixed-length observation period is established using a limit theorem on double array martingales. This is the key step for obtaining central limit theorems for the algorithms with averaging and has interest in its own right.
关键词	perturbation analysis asymptotic efficiency central limit theorems stochastic approximation recursive estimation queueing theory
语种	英语
WOS研究方向	Automation & Control Systems ; Mathematics
WOS类目	Automation & Control Systems ; Mathematics, Applied
WOS记录号	WOS:000083607900010
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/14478
专题	中国科学院数学与系统科学研究院
通讯作者	Tang, QY
作者单位	1.Univ Montreal, Dept Informat & Rech Operat, Montreal, PQ H3C 3J7, Canada 2.Acad Sinica, Inst Syst Sci, Lab Syst & Control, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Tang, QY,L'Ecuyer, P,Chen, HF. Asymptotic efficiency of perturbation-analysis-based stochastic approximation with averaging[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION,1999,37(6):1822-1847.
APA	Tang, QY,L'Ecuyer, P,&Chen, HF.(1999).Asymptotic efficiency of perturbation-analysis-based stochastic approximation with averaging.SIAM JOURNAL ON CONTROL AND OPTIMIZATION,37(6),1822-1847.
MLA	Tang, QY,et al."Asymptotic efficiency of perturbation-analysis-based stochastic approximation with averaging".SIAM JOURNAL ON CONTROL AND OPTIMIZATION 37.6(1999):1822-1847.