IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v64y2016i6p1515-1528.html
   My bibliography  Save this article

On the Convergence Rates of Expected Improvement Methods

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.2016.1494
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.2016.1494?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Huashuai Qu & Ilya O. Ryzhov & Michael C. Fu & Zi Ding, 2015. "Sequential Selection with Unknown Correlation Structures," Operations Research, INFORMS, vol. 63(4), pages 931-948, August.
    3. Chun-Hung Chen & Stephen E. Chick & Loo Hay Lee & Nugroho A. Pujowidianto, 2015. "Ranking and Selection: Efficient Simulation Budget Allocation," International Series in Operations Research & Management Science, in: Michael C Fu (ed.), Handbook of Simulation Optimization, edition 127, chapter 0, pages 45-80, Springer.
    4. Michael C. Fu & Jian-Qiang Hu & Chun-Hung Chen & Xiaoping Xiong, 2007. "Simulation Allocation for Determining the Best Design in the Presence of Correlated Sampling," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 101-111, February.
    5. Ilya O. Ryzhov & Warren B. Powell, 2011. "Information Collection on a Graph," Operations Research, INFORMS, vol. 59(1), pages 188-201, February.
    6. 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.
    7. 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.
    8. Daniel Russo & Benjamin Van Roy, 2014. "Learning to Optimize via Posterior Sampling," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1221-1243, November.
    9. Stephen E. Chick & Koichiro Inoue, 2001. "New Two-Stage and Sequential Procedures for Selecting the Best Simulated System," Operations Research, INFORMS, vol. 49(5), pages 732-743, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Ye Chen & Ilya O. Ryzhov, 2023. "Balancing Optimal Large Deviations in Sequential Selection," Management Science, INFORMS, vol. 69(6), pages 3457-3473, June.
    4. Powell, Warren B., 2019. "A unified framework for stochastic optimization," European Journal of Operational Research, Elsevier, vol. 275(3), pages 795-821.
    5. 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.
    6. 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.
    7. 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.
    8. Daniel Russo, 2020. "Simple Bayesian Algorithms for Best-Arm Identification," Operations Research, INFORMS, vol. 68(6), pages 1625-1647, November.
    9. 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.
    10. Dawei Zhan & Huanlai Xing, 2020. "Expected improvement for expensive optimization: a review," Journal of Global Optimization, Springer, vol. 78(3), pages 507-544, November.
    11. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Juergen Branke & Wen Zhang, 2019. "Identifying efficient solutions via simulation: myopic multi-objective budget allocation for the bi-objective case," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(3), pages 831-865, September.
    2. Daniel Russo, 2020. "Simple Bayesian Algorithms for Best-Arm Identification," Operations Research, INFORMS, vol. 68(6), pages 1625-1647, November.
    3. Jeffrey W. Herrmann & Kunal Mehta, 2020. "Lookahead and Hybrid Sample Allocation Procedures for Multiple Attribute Selection Decisions," Papers 2007.16119, arXiv.org.
    4. Stephen E. Chick & Peter Frazier, 2012. "Sequential Sampling with Economics of Selection Procedures," Management Science, INFORMS, vol. 58(3), pages 550-569, March.
    5. Yijie Peng & Chun-Hung Chen & Michael C. Fu & Jian-Qiang Hu, 2016. "Dynamic Sampling Allocation and Design Selection," INFORMS Journal on Computing, INFORMS, vol. 28(2), pages 195-208, May.
    6. 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.
    7. Bin Han & Ilya O. Ryzhov & Boris Defourny, 2016. "Optimal Learning in Linear Regression with Combinatorial Feature Selection," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 721-735, November.
    8. 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.
    9. Zhongshun Shi & Siyang Gao & Hui Xiao & Weiwei Chen, 2019. "A worst‐case formulation for constrained ranking and selection with input uncertainty," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(8), pages 648-662, December.
    10. Powell, Warren B., 2019. "A unified framework for stochastic optimization," European Journal of Operational Research, Elsevier, vol. 275(3), pages 795-821.
    11. Eric M. Schwartz & Eric T. Bradlow & Peter S. Fader, 2017. "Customer Acquisition via Display Advertising Using Multi-Armed Bandit Experiments," Marketing Science, INFORMS, vol. 36(4), pages 500-522, July.
    12. Ye Chen & Ilya O. Ryzhov, 2023. "Balancing Optimal Large Deviations in Sequential Selection," Management Science, INFORMS, vol. 69(6), pages 3457-3473, June.
    13. Haihui Shen & L. Jeff Hong & Xiaowei Zhang, 2021. "Ranking and Selection with Covariates for Personalized Decision Making," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1500-1519, October.
    14. Huashuai Qu & Ilya O. Ryzhov & Michael C. Fu & Eric Bergerson & Megan Kurka & Ludek Kopacek, 2020. "Learning Demand Curves in B2B Pricing: A New Framework and Case Study," Production and Operations Management, Production and Operations Management Society, vol. 29(5), pages 1287-1306, May.
    15. Saeid Delshad & Amin Khademi, 2020. "Information theory for ranking and selection," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(4), pages 239-253, June.
    16. Groves, Matthew & Branke, Juergen, 2019. "Top-κ selection with pairwise comparisons," European Journal of Operational Research, Elsevier, vol. 274(2), pages 615-626.
    17. 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.
    18. Diana M. Negoescu & Peter I. Frazier & Warren B. Powell, 2011. "The Knowledge-Gradient Algorithm for Sequencing Experiments in Drug Discovery," INFORMS Journal on Computing, INFORMS, vol. 23(3), pages 346-363, August.
    19. Huashuai Qu & Ilya O. Ryzhov & Michael C. Fu & Zi Ding, 2015. "Sequential Selection with Unknown Correlation Structures," Operations Research, INFORMS, vol. 63(4), pages 931-948, August.
    20. Ilya O. Ryzhov & Martijn R. K. Mes & Warren B. Powell & Gerald van den Berg, 2019. "Bayesian Exploration for Approximate Dynamic Programming," Operations Research, INFORMS, vol. 67(1), pages 198-214, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:64:y:2016:i:6:p:1515-1528. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.