# Functional Bandits

arXiv: https://arxiv.org/abs/1405.2432 · HTML: https://mlsanity.com/paper/1405.2432/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 May 2014.

## Built on by (most cited first, 3 of 3)

- [Functional multi-armed bandit and the best function identification problems](https://mlsanity.com/paper/2503.00509/) (2025)
- [Thompson Sampling in Function Spaces via Neural Operators](https://mlsanity.com/paper/2506.21894/) (2025)
- [Beyond Static Bias: Adaptive Multi-Fidelity Bandits with Improving Proxies](https://mlsanity.com/paper/2605.08558/) (2026)

## Abstract (arXiv)

We introduce the functional bandit problem, where the objective is to find an arm that optimises a known functional of the unknown arm-reward distributions. These problems arise in many settings such as maximum entropy methods in natural language processing, and risk-averse decision-making, but current best-arm identification techniques fail in these domains. We propose a new approach, that combines functional estimation and arm elimination, to tackle this problem. This method achieves provably efficient performance guarantees. In addition, we illustrate this method on a number of important functionals in risk management and information theory, and refine our generic theoretical results in those cases.