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 A stochastic approximation algorithm with step-size adaptation
Please use this identifier to cite or link to this item http://hdl.handle.net/10773/4446

title: A stochastic approximation algorithm with step-size adaptation
authors: Cruz, João Pedro Antunes Ferreira da
keywords: stochastic approximation
issue date: 2004
publisher: Springer Verlag
abstract: We consider the following stochastic approximation algorithm of searching for the zero point x∗ of a function ϕ: xt+1 = xt − γtyt, yt = ϕ(xt) + ξt, where yt are observations of ϕ and ξt is the random noise. The step sizes γt of the algorithm are random, the increment γt+1 − γt depending on γt and on yt yt−1 in a rather general form. Generally, it is meant that γt increases as ytyt−1 > 0, and decreases otherwise. It is proved that the algorithm converges to x∗ almost surely. This result generalizes similar results of Kesten (1958) and Plakhov and Almeida (1998), where γt+1 − γt is assumed to depend only on γt and sgn(ytyt−1) and not on the magnitude of ytyt−1.
URI: http://hdl.handle.net/10773/4446
ISSN: 1072-3374
publisher version/DOI: http://www.springerlink.com/content/p8q48v0x60140203/
source: Journal of Mathematical Sciences
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MAT - Artigos

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