Bandit Pareto Set Identification: the Fixed Budget Setting
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913646909587456 |
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| author | Kone, Cyrille Kaufmann, Emilie Richert, Laura |
| author_facet | Kone, Cyrille Kaufmann, Emilie Richert, Laura |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03992 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bandit Pareto Set Identification: the Fixed Budget Setting Kone, Cyrille Kaufmann, Emilie Richert, Laura Machine Learning 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. |
| title | Bandit Pareto Set Identification: the Fixed Budget Setting |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2311.03992 |