A Non-asymptotic Approach to Best-Arm Identification for Gaussian Bandits
Abstract
We propose a new strategy for best-arm identification with fixed confidence of Gaussian variables with bounded means and unit variance. This strategy, called Exploration-Biased Sampling, is not only asymptotically optimal: it is to the best of our knowledge the first strategy with non-asymptotic bounds that asymptotically matches the sample complexity.But the main advantage over other algorithms like Track-and-Stop is an improved behavior regarding exploration: Exploration-Biased Sampling is biased towards exploration in a subtle but natural way that makes it more stable and interpretable. These improvements are allowed by a new analysis of the sample complexity optimization problem, which yields a faster numerical resolution scheme and several quantitative regularity results that we believe of high independent interest.
Keywords
Cite
@article{arxiv.2105.12978,
title = {A Non-asymptotic Approach to Best-Arm Identification for Gaussian Bandits},
author = {Antoine Barrier and Aurélien Garivier and Tomáš Kocák},
journal= {arXiv preprint arXiv:2105.12978},
year = {2022}
}