Stochastic root finding via retrospective approximation

Citation
Hf. Chen et Bw. Schmeiser, Stochastic root finding via retrospective approximation, IIE TRANS, 33(3), 2001, pp. 259-275
Citations number
34
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Engineering Management /General
Journal title
IIE TRANSACTIONS
ISSN journal
0740-817X → ACNP
Volume
33
Issue
3
Year of publication
2001
Pages
259 - 275
Database
ISI
SICI code
0740-817X(200103)33:3<259:SRFVRA>2.0.ZU;2-2
Abstract
Given a user-provided Monte Carlo simulation procedure to estimate a functi on at any specified point, the stochastic root-finding problem is to find t he unique argument value to provide a specified function value. To solve su ch problems, we introduce the family of Retrospective Approximation (RA) al gorithms. RA solves, with decreasing error, a sequence of sample-path equat ions that are based on increasing Monte Carlo sample sizes. Two variations are developed: IRA, in which each sample-path equation is generated indepen dently of the others, and DRA, in which each equation is obtained by append ing new random variates to the previous equation. We prove that such algori thms converge with probability one to the desired solution as the number of iterations grows, discuss implementation issues to obtain good performance in practice without tuning algorithm parameters, provide experimental resu lts for an illustrative application, and argue that IRA dominates DRA in te rms of the generalized mean squared error.