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Implicitly normalized forecaster with clipping for linear and non-linear heavy-tailed multi-armed bandits

Author

Listed:
  • Yuriy Dorn

    (MSU Institute for Artificial Intelligence
    Moscow Institute of Physics and Technology
    Institute for Information Transmission Problems)

  • Nikita Kornilov

    (Moscow Institute of Physics and Technology)

  • Nikolay Kutuzov

    (Moscow Institute of Physics and Technology)

  • Alexander Nazin

    (V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences)

  • Eduard Gorbunov

    (Mohamed bin Zayed University of Artificial Intelligence)

  • Alexander Gasnikov

    (Moscow Institute of Physics and Technology
    Skoltech
    ISP RAS Research Center for Trusted Artificial Intelligence)

Abstract

The Implicitly Normalized Forecaster (INF) algorithm is considered to be an optimal solution for adversarial multi-armed bandit (MAB) problems. However, most of the existing complexity results for INF rely on restrictive assumptions, such as bounded rewards. Recently, a related algorithm was proposed that works for both adversarial and stochastic heavy-tailed MAB settings. However, this algorithm fails to fully exploit the available data. In this paper, we propose a new version of INF called the Implicitly Normalized Forecaster with clipping (INF-clip) for MAB problems with heavy-tailed reward distributions. We establish convergence results under mild assumptions on the rewards distribution and demonstrate that INF-clip is optimal for linear heavy-tailed stochastic MAB problems and works well for non-linear ones. Furthermore, we show that INF-clip outperforms the best-of-both-worlds algorithm in cases where it is difficult to distinguish between different arms.

Suggested Citation

  • Yuriy Dorn & Nikita Kornilov & Nikolay Kutuzov & Alexander Nazin & Eduard Gorbunov & Alexander Gasnikov, 2024. "Implicitly normalized forecaster with clipping for linear and non-linear heavy-tailed multi-armed bandits," Computational Management Science, Springer, vol. 21(1), pages 1-29, June.
    • Handle: RePEc:spr:comgts:v:21:y:2024:i:1:d:10.1007_s10287-023-00500-z
    DOI: 10.1007/s10287-023-00500-z
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