Central Limit Theorems for Stochastic Optimization AlgorithmsUsing Infinitesimal Perturbation Analysis

Authors:
Qian-Yu Tang;Han-Fu Chen
Affiliations:
Département d‘IRO, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal H3C 3J7, Canada;-
Venue:
Discrete Event Dynamic Systems
Year:
2000

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Abstract

Central limit theorems are obtained for the’’perturbation analysis Robbins-Monro single run‘‘ (PARMSR) optimizationalgorithm, with updates either after every L customersor after every busy period, in the context of the optimizationof a GI/GI/1 queue. The PARMSR algorithm is a stochasticapproximation (SA) method for the optimization of infinite-horizonmodels. It is shown that the convergence rate and the asymptoticvariance constant of the optimization algorithm, as a functionof the total computing budget (i.e., total number of customers),are the same for both updating methods, and independent of L,provided that the step sizes of SA are chosen in the (asymptotically)optimal way for each method.