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|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.|
|publisher version/DOI: ||http://www.springerlink.com/content/p8q48v0x60140203/|
|source: ||Journal of Mathematical Sciences|
|appears in collections||CIDMA - Artigos|
MAT - Artigos
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