The Batch Complexity of Bandit Pure Exploration

Adrienne Tuynman, Rémy Degenne
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:60442-60468, 2025.

Abstract

In a fixed-confidence pure exploration problem in stochastic multi-armed bandits, an algorithm iteratively samples arms and should stop as early as possible and return the correct answer to a query about the arms distributions. We are interested in batched methods, which change their sampling behaviour only a few times, between batches of observations. We give an instance-dependent lower bound on the number of batches used by any sample efficient algorithm for any pure exploration task. We then give a general batched algorithm and prove upper bounds on its expected sample complexity and batch complexity. We illustrate both lower and upper bounds on best-arm identification and thresholding bandits.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-tuynman25a, title = {The Batch Complexity of Bandit Pure Exploration}, author = {Tuynman, Adrienne and Degenne, R\'{e}my}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {60442--60468}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/tuynman25a/tuynman25a.pdf}, url = {https://proceedings.mlr.press/v267/tuynman25a.html}, abstract = {In a fixed-confidence pure exploration problem in stochastic multi-armed bandits, an algorithm iteratively samples arms and should stop as early as possible and return the correct answer to a query about the arms distributions. We are interested in batched methods, which change their sampling behaviour only a few times, between batches of observations. We give an instance-dependent lower bound on the number of batches used by any sample efficient algorithm for any pure exploration task. We then give a general batched algorithm and prove upper bounds on its expected sample complexity and batch complexity. We illustrate both lower and upper bounds on best-arm identification and thresholding bandits.} }
Endnote
%0 Conference Paper %T The Batch Complexity of Bandit Pure Exploration %A Adrienne Tuynman %A Rémy Degenne %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-tuynman25a %I PMLR %P 60442--60468 %U https://proceedings.mlr.press/v267/tuynman25a.html %V 267 %X In a fixed-confidence pure exploration problem in stochastic multi-armed bandits, an algorithm iteratively samples arms and should stop as early as possible and return the correct answer to a query about the arms distributions. We are interested in batched methods, which change their sampling behaviour only a few times, between batches of observations. We give an instance-dependent lower bound on the number of batches used by any sample efficient algorithm for any pure exploration task. We then give a general batched algorithm and prove upper bounds on its expected sample complexity and batch complexity. We illustrate both lower and upper bounds on best-arm identification and thresholding bandits.
APA
Tuynman, A. & Degenne, R.. (2025). The Batch Complexity of Bandit Pure Exploration. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:60442-60468 Available from https://proceedings.mlr.press/v267/tuynman25a.html.

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