Simulation-Based Optimization with Stochastic Approximation Using Common Random Numbers

Nathan L. Kleinman, James C. Spall and Daniel Q. Naiman
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Nathan L. Kleinman: Options and Choices, Inc. (OCI), 2232 Dell Range Blvd., Suite 300, Cheyenne, Wyoming 82009
James C. Spall: The Johns Hopkins University Applied Physics Laboratory, Johns Hopkins Road, Laurel, Maryland 20723
Daniel Q. Naiman: The Johns Hopkins University Department of Mathematical Sciences, Baltimore, Maryland 21218

Management Science, 1999, vol. 45, issue 11, 1570-1578

Abstract: The method of Common Random Numbers is a technique used to reduce the variance of difference estimates in simulation optimization problems. These differences are commonly used to estimate gradients of objective functions as part of the process of determining optimal values for parameters of a simulated system. Asymptotic results exist which show that using the Common Random Numbers method in the iterative Finite Difference Stochastic Approximation optimization algorithm (FDSA) can increase the optimal rate of convergence of the algorithm from the typical rate of k -1/3 to the faster k -1/2 , where k is the algorithm's iteration number. Simultaneous Perturbation Stochastic Approximation (SPSA) is a newer and often much more efficient optimization algorithm, and we will show that this algorithm, too, converges faster when the Common Random Numbers method is used. We will also provide multivariate asymptotic covariance matrices for both the SPSA and FDSA errors.

Keywords: Common Random Numbers; Simultaneous Perturbation Stochastic Approximation (SPSA); Finite Difference Stochastic Approximation (FDSA); discrete event dynamic systems (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (8)

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