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Sequential Bayes-Optimal Policies for Multiple Comparisons with a Known Standard

Author

Listed:
  • Jing Xie

    (School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853)

  • Peter I. Frazier

    (School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853)

Abstract

We consider the problem of efficiently allocating simulation effort to determine which of several simulated systems have mean performance exceeding a threshold of known value. Within a Bayesian formulation of this problem, the optimal fully sequential policy for allocating simulation effort is the solution to a dynamic program. When sampling is limited by probabilistic termination or sampling costs, we show that this dynamic program can be solved efficiently, providing a tractable way to compute the Bayes-optimal policy. The solution uses techniques from optimal stopping and multiarmed bandits. We then present further theoretical results characterizing this Bayes-optimal policy, compare it numerically to several approximate policies, and apply it to applications in emergency services and manufacturing.

Suggested Citation

  • Jing Xie & Peter I. Frazier, 2013. "Sequential Bayes-Optimal Policies for Multiple Comparisons with a Known Standard," Operations Research, INFORMS, vol. 61(5), pages 1174-1189, October.
    • Handle: RePEc:inm:oropre:v:61:y:2013:i:5:p:1174-1189
    DOI: 10.1287/opre.2013.1207
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    References listed on IDEAS

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    1. Stephen E. Chick & Noah Gans, 2009. "Economic Analysis of Simulation Selection Problems," Management Science, INFORMS, vol. 55(3), pages 421-437, March.
    2. Stephen E. Chick & Jürgen Branke & Christian Schmidt, 2010. "Sequential Sampling to Myopically Maximize the Expected Value of Information," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 71-80, February.
    3. Victor F. Araman & René Caldentey, 2009. "Dynamic Pricing for Nonperishable Products with Demand Learning," Operations Research, INFORMS, vol. 57(5), pages 1169-1188, October.
    4. Richard Bellman, 1954. "Some Applications of the Theory of Dynamic Programming---A Review," Operations Research, INFORMS, vol. 2(3), pages 275-288, August.
    5. Stephen E. Chick & Peter Frazier, 2012. "Sequential Sampling with Economics of Selection Procedures," Management Science, INFORMS, vol. 58(3), pages 550-569, March.
    6. Peter I. Frazier & Warren B. Powell, 2010. "Paradoxes in Learning and the Marginal Value of Information," Decision Analysis, INFORMS, vol. 7(4), pages 378-403, December.
    7. Barry L. Nelson & David Goldsman, 2001. "Comparisons with a Standard in Simulation Experiments," Management Science, INFORMS, vol. 47(3), pages 449-463, March.
    8. Peter Frazier & Warren Powell & Savas Dayanik, 2009. "The Knowledge-Gradient Policy for Correlated Normal Beliefs," INFORMS Journal on Computing, INFORMS, vol. 21(4), pages 599-613, November.
    9. Sigrún Andradóttir & Seong‐Hee Kim, 2010. "Fully sequential procedures for comparing constrained systems via simulation," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(5), pages 403-421, August.
    10. Matthew S. Maxwell & Mateo Restrepo & Shane G. Henderson & Huseyin Topaloglu, 2010. "Approximate Dynamic Programming for Ambulance Redeployment," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 266-281, May.
    11. Ilya O. Ryzhov & Warren B. Powell & Peter I. Frazier, 2012. "The Knowledge Gradient Algorithm for a General Class of Online Learning Problems," Operations Research, INFORMS, vol. 60(1), pages 180-195, February.
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    Cited by:

    1. Zhongshun Shi & Yijie Peng & Leyuan Shi & Chun-Hung Chen & Michael C. Fu, 2022. "Dynamic Sampling Allocation Under Finite Simulation Budget for Feasibility Determination," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 557-568, January.
    2. Yuwei Zhou & Sigrún Andradóttir & Seong-Hee Kim & Chuljin Park, 2022. "Finding Feasible Systems for Subjective Constraints Using Recycled Observations," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3080-3095, November.
    3. Satyajith Amaran & Nikolaos V. Sahinidis & Bikram Sharda & Scott J. Bury, 2016. "Simulation optimization: a review of algorithms and applications," Annals of Operations Research, Springer, vol. 240(1), pages 351-380, May.

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