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A PAC algorithm in relative precision for bandit problem with costly sampling

Author

Listed:
  • Marie Billaud Friess

    (Nantes Université Centrale Nantes, LMJL, UMR CNRS 6629)

  • Arthur Macherey

    (Nantes Université Centrale Nantes, LMJL, UMR CNRS 6629
    Université Grenoble Alpes)

  • Anthony Nouy

    (Nantes Université Centrale Nantes, LMJL, UMR CNRS 6629)

  • Clémentine Prieur

    (Université Grenoble Alpes)

Abstract

This paper considers the problem of maximizing an expectation function over a finite set, or finite-arm bandit problem. We first propose a naive stochastic bandit algorithm for obtaining a probably approximately correct (PAC) solution to this discrete optimization problem in relative precision, that is a solution which solves the optimization problem up to a relative error smaller than a prescribed tolerance, with high probability. We also propose an adaptive stochastic bandit algorithm which provides a PAC-solution with the same guarantees. The adaptive algorithm outperforms the mean complexity of the naive algorithm in terms of number of generated samples and is particularly well suited for applications with high sampling cost.

Suggested Citation

  • Marie Billaud Friess & Arthur Macherey & Anthony Nouy & Clémentine Prieur, 2022. "A PAC algorithm in relative precision for bandit problem with costly sampling," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(2), pages 161-185, October.
    • Handle: RePEc:spr:mathme:v:96:y:2022:i:2:d:10.1007_s00186-022-00769-x
    DOI: 10.1007/s00186-022-00769-x
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    References listed on IDEAS

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    1. Gilles Stoltz & Sébastien Bubeck & Rémi Munos, 2011. "Pure exploration in finitely-armed and continuous-armed bandits," Post-Print hal-00609550, HAL.
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