Bandit Pareto Set Identification in a Multi-Output Linear Model

AISTATS 2025 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 unkno...

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Bibliographic Details
Main Authors Kone, Cyrille, Kaufmann, Emilie, Richert, Laura
Format Journal Article
LanguageEnglish
Published 06.07.2025
Subjects
Computer Science - Learning
Statistics - Machine Learning
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DOI10.48550/arxiv.2507.04255

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Summary:AISTATS 2025 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$Θ\in \mathbb{R}^{h \times d}$ . 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.
DOI:10.48550/arxiv.2507.04255