Simulation-Based Optimization with Stochastic Approximation Using Common Random Numbers
AbstractThe 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.
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Bibliographic InfoArticle provided by INFORMS in its journal Management Science.
Volume (Year): 45 (1999)
Issue (Month): 11 (November)
Common Random Numbers; Simultaneous Perturbation Stochastic Approximation (SPSA); Finite Difference Stochastic Approximation (FDSA); discrete event dynamic systems;
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- Nicolai, R.P. & Koning, A.J., 2006. "A general framework for statistical inference on discrete event systems," Econometric Institute Research Papers EI 2006-45, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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