Bandit Pareto Set Identification: the Fixed Budget Setting

• URL: http://arxiv.org/abs/2311.03992v1
• Date: Tue, 7 Nov 2023 13:43:18 GMT
• Title: Bandit Pareto Set Identification: the Fixed Budget Setting
• Authors: Cyrille Kone, Emilie Kaufmann, Laura Richert
• Abstract summary: We study a pure exploration problem in a multi-armed bandit model. The goal is to identify the distributions whose mean is not uniformly worse than that of another distribution.
• Score: 12.326452468513228
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: We study a multi-objective pure exploration problem in a multi-armed bandit model. Each arm is associated to an unknown multi-variate distribution and the goal is to identify the distributions whose mean is not uniformly worse than that of another distribution: the Pareto optimal set. We propose and analyze the first algorithms for the \emph{fixed budget} Pareto Set Identification task. We propose Empirical Gap Elimination, a family of algorithms combining a careful estimation of the ``hardness to classify'' each arm in or out of the Pareto set with a generic elimination scheme. We prove that two particular instances, EGE-SR and EGE-SH, have a probability of error that decays exponentially fast with the budget, with an exponent supported by an information theoretic lower-bound. We complement these findings with an empirical study using real-world and synthetic datasets, which showcase the good performance of our algorithms.

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