Bandit Pareto Set Identification: the Fixed Budget Setting

Cyrille Kone, Emilie Kaufmann, Laura Richert
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:2548-2556, 2024.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-kone24a, title = {Bandit {P}areto Set Identification: the Fixed Budget Setting}, author = {Kone, Cyrille and Kaufmann, Emilie and Richert, Laura}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {2548--2556}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/kone24a/kone24a.pdf}, url = {https://proceedings.mlr.press/v238/kone24a.html}, 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.} }
Endnote
%0 Conference Paper %T Bandit Pareto Set Identification: the Fixed Budget Setting %A Cyrille Kone %A Emilie Kaufmann %A Laura Richert %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-kone24a %I PMLR %P 2548--2556 %U https://proceedings.mlr.press/v238/kone24a.html %V 238 %X 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.
APA
Kone, C., Kaufmann, E. & Richert, L.. (2024). Bandit Pareto Set Identification: the Fixed Budget Setting. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:2548-2556 Available from https://proceedings.mlr.press/v238/kone24a.html.

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