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Simulation-Based Optimization with Stochastic Approximation Using Common Random Numbers

Author

Listed:
  • 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)

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.

Suggested Citation

  • Nathan L. Kleinman & James C. Spall & Daniel Q. Naiman, 1999. "Simulation-Based Optimization with Stochastic Approximation Using Common Random Numbers," Management Science, INFORMS, vol. 45(11), pages 1570-1578, November.
    • Handle: RePEc:inm:ormnsc:v:45:y:1999:i:11:p:1570-1578
    DOI: 10.1287/mnsc.45.11.1570
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    References listed on IDEAS

    as
    1. Gal, S. & Rubinstein, R.Y. & Ziv, A., 1984. "On the optimality and efficiency of common random numbers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 26(6), pages 502-512.
    2. Paul Glasserman & David D. Yao, 1992. "Some Guidelines and Guarantees for Common Random Numbers," Management Science, INFORMS, vol. 38(6), pages 884-908, June.
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    3. Angun, M.E., 2004. "Black box simulation optimization : Generalized response surface methodology," Other publications TiSEM 2548e953-54ce-44e2-8c5b-7, Tilburg University, School of Economics and Management.
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