{"ID":2897819,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.04255","arxiv_id":"2507.04255","title":"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 $Θ\\in \\mathbb{R}^{h \\times d}$. 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.","short_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 $Θ\\in \\mathbb{R}^{h \\...","url_abs":"https://arxiv.org/abs/2507.04255","url_pdf":"https://arxiv.org/pdf/2507.04255v1","authors":"[\"Cyrille Kone\",\"Emilie Kaufmann\",\"Laura Richert\"]","published":"2025-07-06T06:14:43Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\"]","methods":"[]","has_code":false}