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On the Convergence Rates of Expected Improvement Methods

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  • Ilya O. Ryzhov

    (Robert H. Smith School of Business, University of Maryland, College Park, Maryland 20742)

Abstract

We consider a ranking and selection problem with independent normal observations, and we analyze the asymptotic sampling rates of expected improvement (EI) methods in this setting. Such methods often perform well in practice, but a tractable analysis of their convergence rates is difficult because of the nonlinearity and nonconvexity of the EI calculations. We present new results indicating that, for known sampling noise, variants of EI produce asymptotic simulation allocations that are essentially identical to those chosen by the optimal computing budget allocation (OCBA) methodology, which is known to yield near-optimal asymptotic performance in ranking and selection. This is the first general equivalence result between EI and OCBA, and it provides insight into the good practical performance of EI. We also derive the limiting allocation for EI under unknown sampling variance.

Suggested Citation

  • Ilya O. Ryzhov, 2016. "On the Convergence Rates of Expected Improvement Methods," Operations Research, INFORMS, vol. 64(6), pages 1515-1528, December.
    • Handle: RePEc:inm:oropre:v:64:y:2016:i:6:p:1515-1528
    DOI: 10.1287/opre.2016.1494
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    References listed on IDEAS

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    Cited by:

    1. Ye Chen & Ilya O. Ryzhov, 2023. "Balancing Optimal Large Deviations in Sequential Selection," Management Science, INFORMS, vol. 69(6), pages 3457-3473, June.
    2. Powell, Warren B., 2019. "A unified framework for stochastic optimization," European Journal of Operational Research, Elsevier, vol. 275(3), pages 795-821.
    3. L. Jeff Hong & Guangxin Jiang & Ying Zhong, 2022. "Solving Large-Scale Fixed-Budget Ranking and Selection Problems," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 2930-2949, November.
    4. Gongbo Zhang & Yijie Peng & Jianghua Zhang & Enlu Zhou, 2023. "Asymptotically Optimal Sampling Policy for Selecting Top- m Alternatives," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1261-1285, November.
    5. 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.
    6. Daniel Russo, 2020. "Simple Bayesian Algorithms for Best-Arm Identification," Operations Research, INFORMS, vol. 68(6), pages 1625-1647, November.
    7. Dawei Zhan & Huanlai Xing, 2020. "Expected improvement for expensive optimization: a review," Journal of Global Optimization, Springer, vol. 78(3), pages 507-544, November.
    8. Yijie Peng & Chun-Hung Chen & Michael C. Fu & Jian-Qiang Hu & Ilya O. Ryzhov, 2021. "Efficient Sampling Allocation Procedures for Optimal Quantile Selection," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 230-245, January.
    9. Ye Chen & Ilya O. Ryzhov, 2020. "Technical Note—Consistency Analysis of Sequential Learning Under Approximate Bayesian Inference," Operations Research, INFORMS, vol. 68(1), pages 295-307, January.
    10. Cheng Li & Siyang Gao & Jianzhong Du, 2023. "Convergence Analysis of Stochastic Kriging-Assisted Simulation with Random Covariates," INFORMS Journal on Computing, INFORMS, vol. 35(2), pages 386-402, March.
    11. Wang, Bo & Zhang, Qiong & Xie, Wei, 2019. "Bayesian sequential data collection for stochastic simulation calibration," European Journal of Operational Research, Elsevier, vol. 277(1), pages 300-316.

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