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Optimal learning for sequential sampling with non-parametric beliefs

Author

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  • Emre Barut

    ()

  • Warren Powell

    ()

Abstract

We propose a sequential learning policy for ranking and selection problems, where we use a non-parametric procedure for estimating the value of a policy. Our estimation approach aggregates over a set of kernel functions in order to achieve a more consistent estimator. Each element in the kernel estimation set uses a different bandwidth to achieve better aggregation. The final estimate uses a weighting scheme with the inverse mean square errors of the kernel estimators as weights. This weighting scheme is shown to be optimal under independent kernel estimators. For choosing the measurement, we employ the knowledge gradient policy that relies on predictive distributions to calculate the optimal sampling point. Our method allows a setting where the beliefs are expected to be correlated but the correlation structure is unknown beforehand. Moreover, the proposed policy is shown to be asymptotically optimal. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Emre Barut & Warren Powell, 2014. "Optimal learning for sequential sampling with non-parametric beliefs," Journal of Global Optimization, Springer, vol. 58(3), pages 517-543, March.
  • Handle: RePEc:spr:jglopt:v:58:y:2014:i:3:p:517-543
    DOI: 10.1007/s10898-013-0050-5
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    File URL: http://hdl.handle.net/10.1007/s10898-013-0050-5
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    References listed on IDEAS

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    1. D. Huang & T. Allen & W. Notz & N. Zeng, 2006. "Global Optimization of Stochastic Black-Box Systems via Sequential Kriging Meta-Models," Journal of Global Optimization, Springer, vol. 34(3), pages 441-466, March.
    2. Stephen E. Chick & Noah Gans, 2009. "Economic Analysis of Simulation Selection Problems," Management Science, INFORMS, vol. 55(3), pages 421-437, March.
    3. Naveed Chehrazi & Thomas A. Weber, 2010. "Monotone Approximation of Decision Problems," Operations Research, INFORMS, vol. 58(4-part-2), pages 1158-1177, August.
    4. Härdle,Wolfgang, 1992. "Applied Nonparametric Regression," Cambridge Books, Cambridge University Press, number 9780521429504, January.
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