Stochastic approximation with state-dependent noise

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	Stochastic approximation with state-dependent noise
	Chen, HF
	2000-10-01
发表期刊	SCIENCE IN CHINA SERIES E-TECHNOLOGICAL SCIENCES
ISSN	1006-9321
卷号	43 期号:5 页码:531-541
摘要	The purpose of stochastic approximation (SA) is to find the roots of f((.)) or the maximizer (minimizer) of L((.)) when the unknown function f((.)) or L((.)) can be observed but with noise. SA is an important tool in dealing with many problems arising from systems and control, whose solutions often rely on convergence of the SA algorithm applied. Here the pathwise convergence of SA algorithms is considered, when the observation noise may depend on state by which we mean those x at which f((.)) or L((.)) are observed. The conditions imposed on the observation noise are the weakest in comparison with the existing ones. When the algorithm is to find the roots of f((.)), the superiority of the condition given in the paper over those used in literature consists in the fact that the present condition is directly verifiable, needless to see the behaviour of the algorithm. When the algorithm is to find the maximizer (minimizer) of L((.)), the present condition allows the observation noise to depend on the state. The conditions imposed on f((.)) and L((.)) are truly general: f((.)) is required to be measurable and locally bounded if the roots of f((.)) are sought, and the gradient of L((.)) is required to be locally Lipschitz continuous if the maximizer (minimizer) of L((.)) is searched.
关键词	stochastic approximation convergence state-dependent noise
语种	英语
WOS研究方向	Engineering ; Materials Science
WOS类目	Engineering, Multidisciplinary ; Materials Science, Multidisciplinary
WOS记录号	WOS:000165146700010
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/15530
专题	系统科学研究所
通讯作者	Chen, HF
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Lab Syst & Control, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Chen, HF. Stochastic approximation with state-dependent noise[J]. SCIENCE IN CHINA SERIES E-TECHNOLOGICAL SCIENCES,2000,43(5):531-541.
APA	Chen, HF.(2000).Stochastic approximation with state-dependent noise.SCIENCE IN CHINA SERIES E-TECHNOLOGICAL SCIENCES,43(5),531-541.
MLA	Chen, HF."Stochastic approximation with state-dependent noise".SCIENCE IN CHINA SERIES E-TECHNOLOGICAL SCIENCES 43.5(2000):531-541.