Multivariate stochastic approximation using a simultaneous perturbation gradient approximation
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The paper presents an SA algorithm that is based on a simultaneous perturbation gradient approximation instead of the standard finite-difference approximation of Keifer-Wolfowitz type procedures that can be significantly more efficient than the standard algorithms in large-dimensional problems.Abstract:
The problem of finding a root of the multivariate gradient equation that arises in function minimization is considered. When only noisy measurements of the function are available, a stochastic approximation (SA) algorithm for the general Kiefer-Wolfowitz type is appropriate for estimating the root. The paper presents an SA algorithm that is based on a simultaneous perturbation gradient approximation instead of the standard finite-difference approximation of Keifer-Wolfowitz type procedures. Theory and numerical experience indicate that the algorithm can be significantly more efficient than the standard algorithms in large-dimensional problems. >read more
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References
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An Introduction to Probability Theory and Its Applications.
Journal ArticleDOI
Stochastic Estimation of the Maximum of a Regression Function
J. Kiefer,Jacob Wolfowitz +1 more
TL;DR: In this article, the authors give a scheme whereby, starting from an arbitrary point, one obtains successively $x_2, x_3, \cdots$ such that the regression function converges to the unknown point in probability as n \rightarrow \infty.
Journal ArticleDOI
Multidimensional Stochastic Approximation Methods
TL;DR: In this paper, a multidimensional stochastic approximation scheme is presented, and conditions are given for these schemes to converge a.s.p.s to the solutions of $k-stochastic equations in $k$ unknowns.
Journal ArticleDOI
Accelerated Stochastic Approximation
TL;DR: In this article, the Robbins-Monro procedure and the Kiefer-Wolfowitz procedure are considered, for which the magnitude of the $n$th step depends on the number of changes in sign in $(X_i - X_{i - 1})$ for n = 2, \cdots, n.