Towards Optimal and Efficient Best Arm Identification in Linear Bandits

TL;DR

This paper introduces a new adaptive algorithm for best arm identification in linear bandits that improves efficiency and theoretical guarantees, outperforming existing methods in sample complexity and practical performance.

Contribution

The paper presents a novel algorithm that generalizes LUCB for linear bandits, offering improved adaptivity, computational efficiency, and theoretical optimality in sample complexity.

Findings

Algorithm is fully adaptive and computationally efficient.

Theoretical analysis shows optimal sample complexity for small arm sets.

Numerical results demonstrate superior performance over existing methods.

Abstract

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.