A PAC algorithm in relative precision for bandit problem with costly sampling
Optimization and Control
2022-06-16 v2 Machine Learning
Machine Learning
Abstract
This paper considers the problem of maximizing an expectation function over a finite set, or finite-arm bandit problem. We first propose a naive stochastic bandit algorithm for obtaining a probably approximately correct (PAC) solution to this discrete optimization problem in relative precision, that is a solution which solves the optimization problem up to a relative error smaller than a prescribed tolerance, with high probability. We also propose an adaptive stochastic bandit algorithm which provides a PAC-solution with the same guarantees. The adaptive algorithm outperforms the mean complexity of the naive algorithm in terms of number of generated samples and is particularly well suited for applications with high sampling cost.
Cite
@article{arxiv.2007.15331,
title = {A PAC algorithm in relative precision for bandit problem with costly sampling},
author = {Marie Billaud-Friess and Arthur Macherey and Anthony Nouy and Clémentine Prieur},
journal= {arXiv preprint arXiv:2007.15331},
year = {2022}
}