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Stochastic approximation with state-dependent noise
Chen, HF
AbstractThe 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.
Keywordstochastic approximation convergence state-dependent noise
WOS Research AreaEngineering ; Materials Science
WOS SubjectEngineering, Multidisciplinary ; Materials Science, Multidisciplinary
WOS IDWOS:000165146700010
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Document Type期刊论文
Corresponding AuthorChen, HF
AffiliationChinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Lab Syst & Control, Beijing 100080, Peoples R China
Recommended Citation
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.
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