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Random sampling: Billiard Walk algorithm

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  • Gryazina, Elena
  • Polyak, Boris

Abstract

Hit-and-Run is known to be one of the best random sampling algorithms, its mixing time is polynomial in dimension. However in practice, the number of steps required to obtain uniformly distributed samples is rather high. We propose a new random walk algorithm based on billiard trajectories. Numerical experiments demonstrate much faster convergence to the uniform distribution.

Suggested Citation

  • Gryazina, Elena & Polyak, Boris, 2014. "Random sampling: Billiard Walk algorithm," European Journal of Operational Research, Elsevier, vol. 238(2), pages 497-504.
    • Handle: RePEc:eee:ejores:v:238:y:2014:i:2:p:497-504
    DOI: 10.1016/j.ejor.2014.03.041
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    References listed on IDEAS

    as
    1. Boris Polyak & Elena Gryazina, 2011. "Randomized methods based on new Monte Carlo schemes for control and optimization," Annals of Operations Research, Springer, vol. 189(1), pages 343-356, September.
    2. Robert L. Smith, 1984. "Efficient Monte Carlo Procedures for Generating Points Uniformly Distributed over Bounded Regions," Operations Research, INFORMS, vol. 32(6), pages 1296-1308, December.
    3. C. G. E. Boender & R. J. Caron & J. F. McDonald & A. H. G. Rinnooy Kan & H. E. Romeijn & R. L. Smith & J. Telgen & A. C. F. Vorst, 1991. "Shake-and-Bake Algorithms for Generating Uniform Points on the Boundary of Bounded Polyhedra," Operations Research, INFORMS, vol. 39(6), pages 945-954, December.
    4. Tervonen, Tommi & van Valkenhoef, Gert & Baştürk, Nalan & Postmus, Douwe, 2013. "Hit-And-Run enables efficient weight generation for simulation-based multiple criteria decision analysis," European Journal of Operational Research, Elsevier, vol. 224(3), pages 552-559.
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    Citations

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    Cited by:

    1. Pavel Shcherbakov & Mingyue Ding & Ming Yuchi, 2021. "Random Sampling Many-Dimensional Sets Arising in Control," Mathematics, MDPI, vol. 9(5), pages 1-16, March.
    2. Xun Shen & Satoshi Ito, 2024. "Approximate Methods for Solving Chance-Constrained Linear Programs in Probability Measure Space," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 150-177, January.
    3. Cyril Bachelard & Apostolos Chalkis & Vissarion Fisikopoulos & Elias Tsigaridas, 2023. "Randomized geometric tools for anomaly detection in stock markets," Post-Print hal-04223511, HAL.
    4. Cyril Bachelard & Apostolos Chalkis & Vissarion Fisikopoulos & Elias Tsigaridas, 2022. "Randomized geometric tools for anomaly detection in stock markets," Papers 2205.03852, arXiv.org, revised May 2022.
    5. Cyril Bachelard & Apostolos Chalkis & Vissarion Fisikopoulos & Elias Tsigaridas, 2024. "Randomized Control in Performance Analysis and Empirical Asset Pricing," Papers 2403.00009, arXiv.org.

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