# Nonparametric Contextual Bandits in an Unknown Metric Space

arXiv: https://arxiv.org/abs/1908.01228 · HTML: https://mlsanity.com/paper/1908.01228/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Aug 2019.

## Built on by (most cited first, 5 of 5)

- [Lipschitz Bandits with Batched Feedback](https://mlsanity.com/paper/2110.09722/) (2021)
- [A Lipschitz Bandits Approach for Continuous Hyperparameter Optimization](https://mlsanity.com/paper/2302.01539/) (2023)
- [Online Algorithms with Uncertainty-Quantified Predictions](https://mlsanity.com/paper/2310.11558/) (2023)
- [Contextual Bandits for Unbounded Context Distributions](https://mlsanity.com/paper/2408.09655/) (2024)
- [From Random Search to Bandit Learning in Metric Measure Spaces](https://mlsanity.com/paper/2305.11509/) (2023)

## Abstract (arXiv)

Consider a nonparametric contextual multi-arm bandit problem where each arm a ∈ [K] is associated to a nonparametric reward function fa: [0,1] → ℝ mapping from contexts to the expected reward. Suppose that there is a large set of arms, yet there is a simple but unknown structure amongst the arm reward functions, e.g. finite types or smooth with respect to an unknown metric space. We present a novel algorithm which learns data-driven similarities amongst the arms, in order to implement adaptive partitioning of the context-arm space for more efficient learning. We provide regret bounds along with simulations that highlight the algorithm's dependence on the local geometry of the reward functions.