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A Scaled Stochastic Approximation Algorithm

Author

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  • Sigrún Andradöttir

    (Department of Industrial Engineering, University of Wisconsin---Madison, 1513 University Avenue, Madison, Wisconsin 53706)

Abstract

Consider a stochastic system of such complexity that its performance can only be evaluated by using simulation or direct experimentation. To optimize the expected performance of such systems as a function of several continuous input parameters (decision variables), we present a "scaled" stochastic approximation algorithm for finding the zero (root) of the gradient of the response function. In each iteration of the scaled algorithm, two independent gradient estimates are sampled at the current estimate of the optimal input-parameter vector to compute a scale-free estimate of the next search direction. We establish sufficient conditions to ensure strong consistency and asymptotic normality of the resulting estimator of the optimal input-parameter vector. Strong consistency is also established for a variant of the scaled algorithm with Kesten's acceleration. An experimental performance comparison of the scaled algorithm and the classical Robbins-Monro algorithm in two simple queueing systems reveals some of the practical advantages of the scaled algorithm.

Suggested Citation

  • Sigrún Andradöttir, 1996. "A Scaled Stochastic Approximation Algorithm," Management Science, INFORMS, vol. 42(4), pages 475-498, April.
    • Handle: RePEc:inm:ormnsc:v:42:y:1996:i:4:p:475-498
    DOI: 10.1287/mnsc.42.4.475
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    Cited by:

    1. Nataša Krejić & Nataša Krklec Jerinkić, 2019. "Spectral projected gradient method for stochastic optimization," Journal of Global Optimization, Springer, vol. 73(1), pages 59-81, January.
    2. Kao, Chiang & Chen, Shih-Pin, 2006. "A stochastic quasi-Newton method for simulation response optimization," European Journal of Operational Research, Elsevier, vol. 173(1), pages 30-46, August.
    3. Chen, Shih-Pin, 2007. "Solving fuzzy queueing decision problems via a parametric mixed integer nonlinear programming method," European Journal of Operational Research, Elsevier, vol. 177(1), pages 445-457, February.
    4. Arsham H., 1998. "Techniques for Monte Carlo Optimizing," Monte Carlo Methods and Applications, De Gruyter, vol. 4(3), pages 181-230, December.
    5. K. Lakshmanan & Shalabh Bhatnagar, 2017. "Quasi-Newton smoothed functional algorithms for unconstrained and constrained simulation optimization," Computational Optimization and Applications, Springer, vol. 66(3), pages 533-556, April.
    6. 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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