# Towards Optimal and Efficient Best Arm Identification in Linear Bandits

arXiv: https://arxiv.org/abs/1911.01695 · HTML: https://mlsanity.com/paper/1911.01695/

## Key facts

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

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

- [Minimax Optimal Fixed-Budget Best Arm Identification in Linear Bandits](https://mlsanity.com/paper/2105.13017/) (2021)
- [Price of Safety in Linear Best Arm Identification](https://mlsanity.com/paper/2309.08709/) (2023)
- [Pure Exploration with Structured Preference Feedback](https://mlsanity.com/paper/2104.05294/) (2021)

## Abstract (arXiv)

We give a new algorithm for best arm identification in linearly parameterised bandits in the fixed confidence setting. The algorithm generalises the well-known LUCB algorithm of Kalyanakrishnan et al. (2012) by playing an arm which minimises a suitable notion of geometric overlap of the statistical confidence set for the unknown parameter, and is fully adaptive and computationally efficient as compared to several state-of-the methods. We theoretically analyse the sample complexity of the algorithm for problems with two and three arms, showing optimality in many cases. Numerical results indicate favourable performance over other algorithms with which we compare.