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Convergence rate of stochastic approximation algorithms in the degenerate case
Chen, HF
1998
Source PublicationSIAM JOURNAL ON CONTROL AND OPTIMIZATION
ISSN0363-0129
Volume36Issue:1Pages:100-114
AbstractLet f(.) be an unknown function whose root x(0) is sought by stochastic approximation (SA). Convergence rate and asymptotic normality are usually established for the nondegenerate case f'(x(0)) not equal 0. This paper demonstrates the convergence rate of SA algorithms for the degenerate case f'(x(0)) = 0. In comparison with the previous work, in this paper no growth rate restriction is imposed on f(.), no statistical property is required for the measurement noise, the general step size is considered, and the result is obtained for the multidimensional case, which is not a straightforward extension of the one-dimensional result. Although the observation noise may be either deterministic or random, the analysis is purely deterministic and elementary.
Keywordstochastic approximation convergence rate
Language英语
WOS Research AreaAutomation & Control Systems ; Mathematics
WOS SubjectAutomation & Control Systems ; Mathematics, Applied
WOS IDWOS:000071962400005
PublisherSIAM PUBLICATIONS
Citation statistics
Cited Times:3[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/13908
Collection中国科学院数学与系统科学研究院
AffiliationChinese Acad Sci, Inst Syst Sci, Lab Syst & Control, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Chen, HF. Convergence rate of stochastic approximation algorithms in the degenerate case[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION,1998,36(1):100-114.
APA Chen, HF.(1998).Convergence rate of stochastic approximation algorithms in the degenerate case.SIAM JOURNAL ON CONTROL AND OPTIMIZATION,36(1),100-114.
MLA Chen, HF."Convergence rate of stochastic approximation algorithms in the degenerate case".SIAM JOURNAL ON CONTROL AND OPTIMIZATION 36.1(1998):100-114.
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