Bandit Pareto Set Identification in a Multi-Output Linear Model

Cyrille Kone, Emilie Kaufmann, Laura Richert
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:1189-1197, 2025.

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 this Paper

BibTeX
@InProceedings{pmlr-v258-kone25b, 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}, pages = {1189--1197}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/kone25b/kone25b.pdf}, url = {https://proceedings.mlr.press/v258/kone25b.html}, 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.} }
Endnote
%0 Conference Paper %T Bandit Pareto Set Identification in a Multi-Output Linear Model %A Cyrille Kone %A Emilie Kaufmann %A Laura Richert %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-kone25b %I PMLR %P 1189--1197 %U https://proceedings.mlr.press/v258/kone25b.html %V 258 %X 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.
APA
Kone, C., Kaufmann, E. & Richert, L.. (2025). Bandit Pareto Set Identification in a Multi-Output Linear Model. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:1189-1197 Available from https://proceedings.mlr.press/v258/kone25b.html.

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