Rate-optimal Design for Anytime Best Arm Identification

Junpei Komiyama, Kyoungseok Jang, Junya Honda

TL;DR: A finite-time analysis of a closed-form anytime algorithm that is minimax optimal up to a constant factor

Abstract:

We consider the best arm identification problem, where the goal is to identify the arm with the highest mean reward from a set of $K$ arms under a limited sampling budget. This problem models many practical scenarios such as A/B testing.
We consider a class of algorithms for this problem, which is provably minimax optimal up to a constant factor. This idea is a generalization of existing works in fixed-budget best arm identification, which are limited to a particular choice of risk measures.
Based on the framework, we propose Almost Tracking, a closed-form algorithm that has a provable guarantee on the popular risk measure.
Unlike existing algorithms, Almost Tracking does not require the total budget in advance nor does it need to discard a significant part of samples, which gives a practical advantage.
Through experiments on synthetic and real-world datasets, we show that our algorithm outperforms existing anytime algorithms as well as fixed-budget algorithms.
Our recommended algorithm for practitioners is found in the final section.

Code Dataset Promise: Yes

Code Dataset Url: https://github.com/jkomiyama/fb_bai_publish/tree/master

Format Confirmation: I agree that I have read and followed the formatting instructions for the camera ready version.

Submission Number: 340