Qualitative Multi-Armed Bandits: A Quantile-Based Approach
Abstract
We formalize and study the multi-armed bandit (MAB) problem in a generalized stochastic setting, in which rewards are not assumed to be numerical. Instead, rewards are measured on a qualitative scale that allows for comparison but invalidates arithmetic operations such as averaging. Correspondingly, instead of characterizing an arm in terms of the mean of the underlying distribution, we opt for using a quantile of that distribution as a representative value. We address the problem of quantile-based online learning both for the case of a finite (pure exploration) and infinite time horizon (cumulative regret minimization). For both cases, we propose suitable algorithms and analyze their properties. These properties are also illustrated by means of first experimental studies.
Cite
Text
Szorenyi et al. "Qualitative Multi-Armed Bandits: A Quantile-Based Approach." International Conference on Machine Learning, 2015.Markdown
[Szorenyi et al. "Qualitative Multi-Armed Bandits: A Quantile-Based Approach." International Conference on Machine Learning, 2015.](https://mlanthology.org/icml/2015/szorenyi2015icml-qualitative/)BibTeX
@inproceedings{szorenyi2015icml-qualitative,
title = {{Qualitative Multi-Armed Bandits: A Quantile-Based Approach}},
author = {Szorenyi, Balazs and Busa-Fekete, Robert and Weng, Paul and Hüllermeier, Eyke},
booktitle = {International Conference on Machine Learning},
year = {2015},
pages = {1660-1668},
volume = {37},
url = {https://mlanthology.org/icml/2015/szorenyi2015icml-qualitative/}
}