Filtered poisson process bandit on a continuum

James A. Grant and Roberto Szechtman

European Journal of Operational Research, 2021, vol. 295, issue 2, 575-586

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.

Keywords: Applied probability; Poisson processes; Multi-Armed bandit; Machine learning (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:295:y:2021:i:2:p:575-586

DOI: 10.1016/j.ejor.2021.03.033

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