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Gaussian process optimization with failures: classification and convergence proof

Author

Listed:
  • François Bachoc

    (Université Paul Sabatier)

  • Céline Helbert

    (Univ. de Lyon)

  • Victor Picheny

    (PROWLER.io)

Abstract
We consider the optimization of a computer model where each simulation either fails or returns a valid output performance. We first propose a new joint Gaussian process model for classification of the inputs (computation failure or success) and for regression of the performance function. We provide results that allow for a computationally efficient maximum likelihood estimation of the covariance parameters, with a stochastic approximation of the likelihood gradient. We then extend the classical improvement criterion to our setting of joint classification and regression. We provide an efficient computation procedure for the extended criterion and its gradient. We prove the almost sure convergence of the global optimization algorithm following from this extended criterion. We also study the practical performances of this algorithm, both on simulated data and on a real computer model in the context of automotive fan design.

Suggested Citation

  • François Bachoc & Céline Helbert & Victor Picheny, 2020. "Gaussian process optimization with failures: classification and convergence proof," Journal of Global Optimization, Springer, vol. 78(3), pages 483-506, November.
    • Handle: RePEc:spr:jglopt:v:78:y:2020:i:3:d:10.1007_s10898-020-00920-0
    DOI: 10.1007/s10898-020-00920-0
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    References listed on IDEAS

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    1. Z. I. Botev, 2017. "The normal law under linear restrictions: simulation and estimation via minimax tilting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 125-148, January.
    2. Antanas Žilinskas & James Calvin, 2019. "Bi-objective decision making in global optimization based on statistical models," Journal of Global Optimization, Springer, vol. 74(4), pages 599-609, August.
    3. Roustant, Olivier & Ginsbourger, David & Deville, Yves, 2012. "DiceKriging, DiceOptim: Two R Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i01).
    Full references (including those not matched with items on IDEAS)

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