NDLI: Convergence of parameter sensitivity estimates in a stochastic experiment

Content Provider	IEEE Xplore Digital Library
Author	Xi-Ren Cao
Copyright Year	1984
Description	Author affiliation: Harvard University, Cambridge, MA (Xi-Ren Cao)
Abstract	To reduce the error in estimating the gradient (parameter sensitivity) of an unknown function is of great importance in stochastic optimization problems. Three kinds of parameter sensitivity estimates using the Monte Carlo method are discussed in this paper. The estimates depend on the number of replications, N, and the change in parameter, ¿v. The convergence properties as N¿¿ and ¿v¿0 for these estimates are obtained. The result explains many theoretical and practical issues in the study of discrete event dynamic systems, as well as continuous dynamic systems, by the Monte Carlo method. It is proved that an estimate based on averaging the gradients calculated along each sample path by a perturbation of the path is much better than the other estimates if the output functions are uniformly differentiable with probability one (w.p.1). It is also concluded that in computer simulations one should always choose the same seed for both v and v+¿v in estimating the parameter sensitivity. Combining the results in this paper with existing stochastic approximation algorithms may yield algorithms with faster convergence.
Starting Page	965
Ending Page	970
File Size	627181
Page Count	6
File Format	PDF
DOI	10.1109/CDC.1984.272158
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1984-12-12
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Convergence Parameter estimation Stochastic processes Computational modeling Computer simulation Approximation algorithms Random variables Error correction System performance Zinc
Content Type	Text
Resource Type	Article

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