Nearly Optimal Best Arm Identification for Semiparametric Bandits

Seok-Jin Kim
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:4402-4410, 2026.

Abstract

We study fixed-confidence Best Arm Identification (BAI) in semiparametric bandits, where rewards are linear in arm features plus an unknown additive baseline shift. Unlike linear-bandit BAI, this setting requires orthogonalized regression, and its instance-optimal sample complexity has remained open. For the transductive setting, we establish an attainable instance-dependent lower bound characterized by the corresponding linear-bandit complexity on shifted features. We then propose a computationally efficient phase-elimination algorithm based on a new $\mathcal{X}\mathcal{Y}$-design for orthogonalized regression. Our analysis yields a nearly optimal high-probability sample-complexity upper bound, up to log factors and an additive $d^2$ term, and experiments on synthetic instances and the Jester dataset show clear gains over prior baselines.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-kim26d, title = { Nearly Optimal Best Arm Identification for Semiparametric Bandits }, author = {Kim, Seok-Jin}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {4402--4410}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/kim26d/kim26d.pdf}, url = {https://proceedings.mlr.press/v300/kim26d.html}, abstract = { We study fixed-confidence Best Arm Identification (BAI) in semiparametric bandits, where rewards are linear in arm features plus an unknown additive baseline shift. Unlike linear-bandit BAI, this setting requires orthogonalized regression, and its instance-optimal sample complexity has remained open. For the transductive setting, we establish an attainable instance-dependent lower bound characterized by the corresponding linear-bandit complexity on shifted features. We then propose a computationally efficient phase-elimination algorithm based on a new $\mathcal{X}\mathcal{Y}$-design for orthogonalized regression. Our analysis yields a nearly optimal high-probability sample-complexity upper bound, up to log factors and an additive $d^2$ term, and experiments on synthetic instances and the Jester dataset show clear gains over prior baselines. } }
Endnote
%0 Conference Paper %T Nearly Optimal Best Arm Identification for Semiparametric Bandits %A Seok-Jin Kim %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-kim26d %I PMLR %P 4402--4410 %U https://proceedings.mlr.press/v300/kim26d.html %V 300 %X We study fixed-confidence Best Arm Identification (BAI) in semiparametric bandits, where rewards are linear in arm features plus an unknown additive baseline shift. Unlike linear-bandit BAI, this setting requires orthogonalized regression, and its instance-optimal sample complexity has remained open. For the transductive setting, we establish an attainable instance-dependent lower bound characterized by the corresponding linear-bandit complexity on shifted features. We then propose a computationally efficient phase-elimination algorithm based on a new $\mathcal{X}\mathcal{Y}$-design for orthogonalized regression. Our analysis yields a nearly optimal high-probability sample-complexity upper bound, up to log factors and an additive $d^2$ term, and experiments on synthetic instances and the Jester dataset show clear gains over prior baselines.
APA
Kim, S.. (2026). Nearly Optimal Best Arm Identification for Semiparametric Bandits . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:4402-4410 Available from https://proceedings.mlr.press/v300/kim26d.html.

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