Bandit Pareto Set Identification in a Multi-Output Linear Model
Abstract
We study the Pareto Set Identification (PSI) problem in a structured multi-output linear bandit model. In this setting, each arm is associated a feature vector belonging to $\mathbb{R}^h$ and its mean vector in $\mathbb{R}^d$ linearly depends on this feature vector through a common unknown matrix $\Theta \in \mathbb{R}^{h \times d}$. The goal is to identify the set of non-dominated arms by adaptively collecting samples from the arms. We introduce and analyze the first optimal design-based algorithms for PSI, providing nearly optimal guarantees in both the fixed-budget and the fixed-confidence settings. Notably, we show that the difficulty of these tasks mainly depends on the sub-optimality gaps of $h$ arms only. Our theoretical results are supported by an extensive benchmark on synthetic and real-world datasets.
Cite
Text
Kone et al. "Bandit Pareto Set Identification in a Multi-Output Linear Model." Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, 2025.Markdown
[Kone et al. "Bandit Pareto Set Identification in a Multi-Output Linear Model." Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, 2025.](https://mlanthology.org/aistats/2025/kone2025aistats-bandit/)BibTeX
@inproceedings{kone2025aistats-bandit,
title = {{Bandit Pareto Set Identification in a Multi-Output Linear Model}},
author = {Kone, Cyrille and Kaufmann, Emilie and Richert, Laura},
booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics},
year = {2025},
pages = {1189-1197},
volume = {258},
url = {https://mlanthology.org/aistats/2025/kone2025aistats-bandit/}
}