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Filtered poisson process bandit on a continuum

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  • Grant, James A.
  • Szechtman, Roberto

Abstract

We consider a version of the continuum armed bandit where an action induces a filtered realisation of a non-homogeneous Poisson process. Point data in the filtered sample are then revealed to the decision-maker, whose reward is the total number of revealed points. Using knowledge of the function governing the filtering, but without knowledge of the Poisson intensity function, the decision-maker seeks to maximise the expected number of revealed points over T rounds. We propose an upper confidence bound algorithm for this problem utilising data-adaptive discretisation of the action space. This approach enjoys O˜(T2/3) regret under a Lipschitz assumption on the reward function. We provide lower bounds on the regret of any algorithm for the problem, via new lower bounds for related finite-armed bandits, and show that the orders of the upper and lower bounds match up to a logarithmic factor.

Suggested Citation

  • Grant, James A. & Szechtman, Roberto, 2021. "Filtered poisson process bandit on a continuum," European Journal of Operational Research, Elsevier, vol. 295(2), pages 575-586.
    • Handle: RePEc:eee:ejores:v:295:y:2021:i:2:p:575-586
    DOI: 10.1016/j.ejor.2021.03.033
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    References listed on IDEAS

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    1. Grant, James A. & Leslie, David S. & Glazebrook, Kevin & Szechtman, Roberto & Letchford, Adam N., 2020. "Adaptive policies for perimeter surveillance problems," European Journal of Operational Research, Elsevier, vol. 283(1), pages 265-278.
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    Cited by:

    1. Agrawal, Priyank & Tulabandhula, Theja & Avadhanula, Vashist, 2023. "A tractable online learning algorithm for the multinomial logit contextual bandit," European Journal of Operational Research, Elsevier, vol. 310(2), pages 737-750.

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