Filtered Poisson Process Bandit on a Continuum

Grant, James A. and Szechtman, Roberto (2020) Filtered Poisson Process Bandit on a Continuum. arXiv.org.

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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(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.

Item Type:
Journal Article
Journal or Publication Title:
arXiv.org
Subjects:
ID Code:
147409
Deposited By:
Deposited On:
12 Oct 2020 15:30
Refereed?:
No
Published?:
Published
Last Modified:
31 Oct 2020 07:20