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Robust Analysis in Stochastic Simulation: Computation and Performance Guarantees

Author

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  • Soumyadip Ghosh

    (IBM Research AI, IBM T.J. Watson Research Center, Yorktown Heights, New York 10598)

  • Henry Lam

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

Abstract

Any performance analysis based on stochastic simulation is subject to the errors inherent in misspecifying the modeling assumptions, particularly the input distributions. In situations with little support from data, we investigate the use of worst-case analysis to analyze these errors, by representing the partial, nonparametric knowledge of the input models via optimization constraints. We study the performance and robustness guarantees of this approach. We design and analyze a numerical scheme for solving a general class of simulation objectives and uncertainty specifications. The key steps involve a randomized discretization of the probability spaces, a simulable unbiased gradient estimator using a nonparametric analog of the likelihood ratio method, and a Frank-Wolfe (FW) variant of the stochastic approximation (SA) method (which we call FWSA) run on the space of input probability distributions. A convergence analysis for FWSA on nonconvex problems is provided. We test the performance of our approach via several numerical examples.

Suggested Citation

  • Soumyadip Ghosh & Henry Lam, 2019. "Robust Analysis in Stochastic Simulation: Computation and Performance Guarantees," Operations Research, INFORMS, vol. 67(1), pages 232-249, January.
    • Handle: RePEc:inm:oropre:v:67:y:2019:i:1:p:232-249
    DOI: 10.1287/opre.2018.1765
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    as
    1. John R. Birge & Roger J.-B. Wets, 1987. "Computing Bounds for Stochastic Programming Problems by Means of a Generalized Moment Problem," Mathematics of Operations Research, INFORMS, vol. 12(1), pages 149-162, February.
    2. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    3. Aharon Ben-Tal & Dick den Hertog & Anja De Waegenaere & Bertrand Melenberg & Gijs Rennen, 2013. "Robust Solutions of Optimization Problems Affected by Uncertain Probabilities," Management Science, INFORMS, vol. 59(2), pages 341-357, April.
    4. Paul Glasserman & Xingbo Xu, 2013. "Robust Portfolio Control with Stochastic Factor Dynamics," Operations Research, INFORMS, vol. 61(4), pages 874-893, August.
    5. James E. Smith, 1995. "Generalized Chebychev Inequalities: Theory and Applications in Decision Analysis," Operations Research, INFORMS, vol. 43(5), pages 807-825, October.
    6. Pengyu Qian & Zizhuo Wang & Zaiwen Wen, 2015. "A Composite Risk Measure Framework for Decision Making under Uncertainty," Papers 1501.01126, arXiv.org.
    7. Rubinstein, Reuven Y., 1986. "The score function approach for sensitivity analysis of computer simulation models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 28(5), pages 351-379.
    8. Henry Lam, 2018. "Sensitivity to Serial Dependency of Input Processes: A Robust Approach," Management Science, INFORMS, vol. 64(3), pages 1311-1327, March.
    9. Andrew E. B. Lim & J. George Shanthikumar, 2007. "Relative Entropy, Exponential Utility, and Robust Dynamic Pricing," Operations Research, INFORMS, vol. 55(2), pages 198-214, April.
    10. James E. Smith, 1993. "Moment Methods for Decision Analysis," Management Science, INFORMS, vol. 39(3), pages 340-358, March.
    11. Soumyadip Ghosh & Shane G. Henderson, 2002. "Chessboard Distributions and Random Vectors with Specified Marginals and Covariance Matrix," Operations Research, INFORMS, vol. 50(5), pages 820-834, October.
    12. Yuhong Xu, 2014. "Robust valuation and risk measurement under model uncertainty," Papers 1407.8024, arXiv.org.
    13. Philip M. Lurie & Matthew S. Goldberg, 1998. "An Approximate Method for Sampling Correlated Random Variables from Partially-Specified Distributions," Management Science, INFORMS, vol. 44(2), pages 203-218, February.
    14. Erick Delage & Yinyu Ye, 2010. "Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems," Operations Research, INFORMS, vol. 58(3), pages 595-612, June.
    15. Wolfram Wiesemann & Daniel Kuhn & Melvyn Sim, 2014. "Distributionally Robust Convex Optimization," Operations Research, INFORMS, vol. 62(6), pages 1358-1376, December.
    16. Garud N. Iyengar, 2005. "Robust Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 257-280, May.
    17. Huan Xu & Shie Mannor, 2012. "Distributionally Robust Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 37(2), pages 288-300, May.
    18. Paul Glasserman & Linan Yang, 2018. "Bounding Wrong†Way Risk In Cva Calculation," Mathematical Finance, Wiley Blackwell, vol. 28(1), pages 268-305, January.
    19. Stephen E. Chick, 2001. "Input Distribution Selection for Simulation Experiments: Accounting for Input Uncertainty," Operations Research, INFORMS, vol. 49(5), pages 744-758, October.
    20. Marguerite Frank & Philip Wolfe, 1956. "An algorithm for quadratic programming," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 95-110, March.
    21. Joel Goh & Melvyn Sim, 2010. "Distributionally Robust Optimization and Its Tractable Approximations," Operations Research, INFORMS, vol. 58(4-part-1), pages 902-917, August.
    22. Wei Xie & Barry L. Nelson & Russell R. Barton, 2014. "A Bayesian Framework for Quantifying Uncertainty in Stochastic Simulation," Operations Research, INFORMS, vol. 62(6), pages 1439-1452, December.
    23. Eunhye Song & Barry L. Nelson, 2015. "Quickly Assessing Contributions to Input Uncertainty," IISE Transactions, Taylor & Francis Journals, vol. 47(9), pages 893-909, September.
    24. Martin I. Reiman & Alan Weiss, 1989. "Sensitivity Analysis for Simulations via Likelihood Ratios," Operations Research, INFORMS, vol. 37(5), pages 830-844, October.
    25. Arnab Nilim & Laurent El Ghaoui, 2005. "Robust Control of Markov Decision Processes with Uncertain Transition Matrices," Operations Research, INFORMS, vol. 53(5), pages 780-798, October.
    26. Paul Glasserman & Xingbo Xu, 2014. "Robust risk measurement and model risk," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 29-58, January.
    27. Zhaolin Hu & Jing Cao & L. Jeff Hong, 2012. "Robust Simulation of Global Warming Policies Using the DICE Model," Management Science, INFORMS, vol. 58(12), pages 2190-2206, December.
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