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 |
Author: | Cruz, João Pedro Antunes Ferreira da Plakhov |
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. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/4446 |
ISSN: | 1072-3374 |
Publisher Version: | http://www.springerlink.com/content/p8q48v0x60140203/ |
Appears in Collections: | CIDMA - Artigos DMat - Artigos |
Files in This Item:
File | Description | Size | Format | |
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2004_PLAKHOV_CRUZ_stochastic.pdf | Documento principal | 129.47 kB | Adobe PDF |
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