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Towards Gaussian Process-based Optimization with Finite Time Horizon

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mODa 9 – Advances in Model-Oriented Design and Analysis

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

Abstract

During the last decade, Kriging-based sequential optimization algorithms have become standard methods in computer experiments. These algorithms rely on the iterative maximization of sampling criteria such as the Expected Improvement (EI), which takes advantage of Kriging conditional distributions to make an explicit trade-off between promising and uncertain points in the search space. We have recently worked on a multipoint EI criterion meant to choose simultaneously several points for synchronous parallel computation. The results presented in this article concern sequential procedures with a fixed number of iterations. We show that maximizing the usual EI at each iteration is suboptimal. In essence, the latter amounts to considering the current iteration as the last one. This work formulates the problem of optimal strategy for finite horizon sequential optimization, provides the solution to this problem in terms of a new multipoint EI, and illustrates the suboptimality of maximizing the 1-point EI at each iteration on the basis of a first counter-example.

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References

  • Auger, A. and O. Teytaud (2010). Continuous lunches are free plus the design of optimal optimization algorithms. Algorithmica 57, 121–146.

    Article  MATH  Google Scholar 

  • Bertsekas, D. (2007). Dynamic Programming and Optimal Control, Vol. 1. Athena Scientific, Belmont, MA.

    Google Scholar 

  • Ginsbourger, D., R. Le Riche, and L. Carraro (2010). Computational Intelligence in Expensive Optimization Problems, Chapter “Kriging is well-suited to parallelize optimization”. Studies in Evolutionary Learning and Optimization. Springer-Verlag.

    Google Scholar 

  • Jones, D., M. Schonlau, and W. Welch (1998). Efficient global optimization of expensive black-box functions. Journal of Global Optimization 13, 455–492.

    Article  MATH  MathSciNet  Google Scholar 

  • Mockus, J. (1988). Bayesian Approach to Global Optimization. Amsterdam: Kluwer.

    Google Scholar 

  • Powell, W. (2007). Approximate Dynamic Programming. Solving the Curses of Dimensionality. New York: Wiley.

    Book  MATH  Google Scholar 

  • Rasmussen, C. and K. Williams (2006). Gaussian Processes for Machine Learning. Boston, MA: M.I.T. Press.

    MATH  Google Scholar 

  • Schonlau, M. (1997). Computer Experiments and Global Optimization. Ph.D. thesis, University of Waterloo, Canada.

    Google Scholar 

  • Stein, M. (1999). Interpolation of Spatial Data, Some Theory for Kriging. Springer.

    Google Scholar 

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Acknowledgements

This work was funded by the Optimisation Multi-Disciplinaire (OMD) project of the French Research Agency (ANR). The authors would like to thank Julien Bect (Ecole Supérieure d’Electricité) for providing them with the related results of Mockus (1988).

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Correspondence to David Ginsbourger .

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Ginsbourger, D., Le Riche, R. (2010). Towards Gaussian Process-based Optimization with Finite Time Horizon. In: Giovagnoli, A., Atkinson, A., Torsney, B., May, C. (eds) mODa 9 – Advances in Model-Oriented Design and Analysis. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2410-0_12

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