# Filtered Poisson Process Bandit on a Continuum

arXiv: https://arxiv.org/abs/2007.09966 · HTML: https://mlsanity.com/paper/2007.09966/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jul 2020.

## Built on by (most cited first, 2 of 2)

- [Efficient Generalized Low-Rank Tensor Contextual Bandits](https://mlsanity.com/paper/2311.01771/) (2023)
- [A Unified Regularization Approach to High-Dimensional Generalized Tensor Bandits](https://mlsanity.com/paper/2501.10722/) (2025)

## Abstract (arXiv)

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.