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Convergence Rates of Finite-Difference Sensitivity Estimates for Stochastic Systems

Author

Listed:
  • Michael A. Zazanis

    (Northwestern University, Evanston, Illinois)

  • Rajan Suri

    (University of Wisconsin, Madison, Wisconsin)

Abstract

A mean square error analysis of finite-difference sensitivity estimators for stochastic systems is presented and an expression for the optimal size of the increment is derived. The asymptotic behavior of the optimal increments, and the behavior of the corresponding optimal finite-difference (FD) estimators are investigated for finite-horizon experiments. Steady-state estimation is also considered for regenerative systems and in this context a convergence analysis of ratio estimators is presented. The use of variance reduction techniques for these FD estimates, such as common random numbers in simulation experiments, is not considered here. In the case here, direct gradient estimation techniques (such as perturbation analysis and likelihood ratio methods) whenever applicable, are shown to converge asymptotically faster than the optimal FD estimators.

Suggested Citation

  • Michael A. Zazanis & Rajan Suri, 1993. "Convergence Rates of Finite-Difference Sensitivity Estimates for Stochastic Systems," Operations Research, INFORMS, vol. 41(4), pages 694-703, August.
    • Handle: RePEc:inm:oropre:v:41:y:1993:i:4:p:694-703
    DOI: 10.1287/opre.41.4.694
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    Cited by:

    1. Ebru Angün & Jack Kleijnen, 2012. "An Asymptotic Test of Optimality Conditions in Multiresponse Simulation Optimization," INFORMS Journal on Computing, INFORMS, vol. 24(1), pages 53-65, February.
    2. R. C. M. Brekelmans & L. T. Driessen & H. J. M. Hamers & D. den. Hertog, 2005. "Gradient Estimation Schemes for Noisy Functions," Journal of Optimization Theory and Applications, Springer, vol. 126(3), pages 529-551, September.
    3. Borgonovo, Emanuele & Rabitti, Giovanni, 2023. "Screening: From tornado diagrams to effective dimensions," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1200-1211.

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