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Filtered Poisson process bandit on a continuum

Research output: Contribution to journalJournal articlepeer-review

E-pub ahead of print
<mark>Journal publication date</mark>24/03/2021
<mark>Journal</mark>European Journal of Operational Research
Number of pages26
Publication StatusE-pub ahead of print
Early online date24/03/21
<mark>Original language</mark>English

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 \tilde{O}(T^(2/3)) 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.