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Asymptotic efficiency of perturbation-analysis-based stochastic approximation with averaging
Tang, QY; L'Ecuyer, P; Chen, HF
1999
Source PublicationSIAM JOURNAL ON CONTROL AND OPTIMIZATION
ISSN0363-0129
Volume37Issue:6Pages:1822-1847
AbstractCentral 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.
Keywordperturbation analysis asymptotic efficiency central limit theorems stochastic approximation recursive estimation queueing theory
Language英语
WOS Research AreaAutomation & Control Systems ; Mathematics
WOS SubjectAutomation & Control Systems ; Mathematics, Applied
WOS IDWOS:000083607900010
PublisherSIAM PUBLICATIONS
Citation statistics
Cited Times:9[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/14478
Collection中国科学院数学与系统科学研究院
Affiliation1.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
Recommended Citation
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.
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