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Stochastic derivative-free optimization using a trust region framework

Author

Listed:
  • Jeffrey Larson

    (Argonne National Laboratory)

  • Stephen C. Billups

    (University of Colorado Denver)

Abstract

This paper presents a trust region algorithm to minimize a function f when one has access only to noise-corrupted function values $$\bar{f}$$ f ¯ . The model-based algorithm dynamically adjusts its step length, taking larger steps when the model and function agree and smaller steps when the model is less accurate. The method does not require the user to specify a fixed pattern of points used to build local models and does not repeatedly sample points. If f is sufficiently smooth and the noise is independent and identically distributed with mean zero and finite variance, we prove that our algorithm produces iterates such that the corresponding function gradients converge in probability to zero. We present a prototype of our algorithm that, while simplistic in its management of previously evaluated points, solves benchmark problems in fewer function evaluations than do existing stochastic approximation methods.

Suggested Citation

  • Jeffrey Larson & Stephen C. Billups, 2016. "Stochastic derivative-free optimization using a trust region framework," Computational Optimization and Applications, Springer, vol. 64(3), pages 619-645, July.
    • Handle: RePEc:spr:coopap:v:64:y:2016:i:3:d:10.1007_s10589-016-9827-z
    DOI: 10.1007/s10589-016-9827-z
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    References listed on IDEAS

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    1. Fabian Bastin & Cinzia Cirillo & Philippe Toint, 2006. "An adaptive Monte Carlo algorithm for computing mixed logit estimators," Computational Management Science, Springer, vol. 3(1), pages 55-79, January.
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    Citations

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    Cited by:

    1. Qi Fan & Jiaqiao Hu, 2018. "Surrogate-Based Promising Area Search for Lipschitz Continuous Simulation Optimization," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 677-693, November.
    2. Charles Audet & Kwassi Joseph Dzahini & Michael Kokkolaras & Sébastien Le Digabel, 2021. "Stochastic mesh adaptive direct search for blackbox optimization using probabilistic estimates," Computational Optimization and Applications, Springer, vol. 79(1), pages 1-34, May.
    3. Andrea Brilli & Morteza Kimiaei & Giampaolo Liuzzi & Stefano Lucidi, 2024. "Worst Case Complexity Bounds for Linesearch-Type Derivative-Free Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 419-454, October.
    4. Kwassi Joseph Dzahini, 2022. "Expected complexity analysis of stochastic direct-search," Computational Optimization and Applications, Springer, vol. 81(1), pages 179-200, January.
    5. V. Kungurtsev & F. Rinaldi, 2021. "A zeroth order method for stochastic weakly convex optimization," Computational Optimization and Applications, Springer, vol. 80(3), pages 731-753, December.
    6. Fengqiao Luo & Jeffrey Larson, 2024. "An Empirical Quantile Estimation Approach for Chance-Constrained Nonlinear Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 767-809, October.

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