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Hesitant adaptive search with estimation and quantile adaptive search for global optimization with noise

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  • Zelda B. Zabinsky

    (University of Washington)

  • David D. Linz

    (University of Washington)

Abstract

Adaptive random search approaches have been shown to be effective for global optimization problems, where under certain conditions, the expected performance time increases only linearly with dimension. However, previous analyses assume that the objective function can be observed directly. We consider the case where the objective function must be estimated, often using a noisy function, as in simulation. We present a finite-time analysis of algorithm performance that combines estimation with a sampling distribution. We present a framework called Hesitant Adaptive Search with Estimation, and derive an upper bound on function evaluations that is cubic in dimension, under certain conditions. We extend the framework to Quantile Adaptive Search with Estimation, which focuses sampling points from a series of nested quantile level sets. The analyses suggest that computational effort is better expended on sampling improving points than refining estimates of objective function values during the progress of an adaptive search algorithm.

Suggested Citation

  • Zelda B. Zabinsky & David D. Linz, 2023. "Hesitant adaptive search with estimation and quantile adaptive search for global optimization with noise," Journal of Global Optimization, Springer, vol. 87(1), pages 31-55, September.
    • Handle: RePEc:spr:jglopt:v:87:y:2023:i:1:d:10.1007_s10898-023-01307-7
    DOI: 10.1007/s10898-023-01307-7
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    References listed on IDEAS

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    1. Y-C Ho & C G Cassandras & C-H Chen & L Dai, 2000. "Ordinal optimisation and simulation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(4), pages 490-500, April.
    2. Zelda Zabinsky & David Bulger & Charoenchai Khompatraporn, 2010. "Stopping and restarting strategy for stochastic sequential search in global optimization," Journal of Global Optimization, Springer, vol. 46(2), pages 273-286, February.
    3. G. R. Wood & D. W. Bulger & W. P. Baritompa & D. L. J. Alexander, 2006. "Backtracking Adaptive Search: Distribution of Number of Iterations to Convergence," Journal of Optimization Theory and Applications, Springer, vol. 128(3), pages 547-562, March.
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