Abstract
The aim of this paper is to present a rate of convergence theorem for a class of stochastic approximation processes for function minimization developed by J. Spa11 in [Spa92]. The main feature of this method is a new way of estimating the gradient using only two measurements at properly selected random parameter values. The main advances of the present paper is that a crucial boundedness hypothesis of [Spa92] is removed by forcing the estimator to stay in a bounded domain and we get the rate of convergence of higher order moments of the estimation error. The rate that we get is identical with the normalization that is used in proving asymptotic normality of the estimator sequence (cf. Proposition 2 in [Spa92]).
This work was supported by a grant from The Johns Hopkins University, Applied Physics Laboratory Independent Research and Development Program and by the National Research Foundation of Hungary (OTKA) under Grant no. 20984
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Gerencsér, L. (1997). Rate of Convergence of Moments of Spall’s SPSA Method. In: Stochastic Differential and Difference Equations. Progress in Systems and Control Theory, vol 23. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1980-4_7
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DOI: https://doi.org/10.1007/978-1-4612-1980-4_7
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7365-3
Online ISBN: 978-1-4612-1980-4
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