Nearly Instance Optimal Sample Complexity Bounds for Top-k Arm Selection

Lijie Chen, Jian Li, Mingda Qiao
Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54:101-110, 2017.

Abstract

In the Best-k-Arm problem, we are given n stochastic bandit arms, each associated with an unknown reward distribution. We are required to identify the k arms with the largest means by taking as few samples as possible. In this paper, we make progress towards a complete characterization of the instance-wise sample complexity bounds for the Best-k-Arm problem. On the lower bound side, we obtain a novel complexity term to measure the sample complexity that every Best-k-Arm instance requires. This is derived by an interesting and nontrivial reduction from the Best-1-Arm problem. We also provide an elimination-based algorithm that matches the instance-wise lower bound within doubly-logarithmic factors. The sample complexity of our algorithm strictly dominates the state-of-the-art for Best-k-Arm (module constant factors).

Cite this Paper

BibTeX
@InProceedings{pmlr-v54-chen17a, title = {{Nearly Instance Optimal Sample Complexity Bounds for Top-k Arm Selection}}, author = {Chen, Lijie and Li, Jian and Qiao, Mingda}, booktitle = {Proceedings of the 20th International Conference on Artificial Intelligence and Statistics}, pages = {101--110}, year = {2017}, editor = {Singh, Aarti and Zhu, Jerry}, volume = {54}, series = {Proceedings of Machine Learning Research}, month = {20--22 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v54/chen17a/chen17a.pdf}, url = {https://proceedings.mlr.press/v54/chen17a.html}, abstract = {In the Best-k-Arm problem, we are given n stochastic bandit arms, each associated with an unknown reward distribution. We are required to identify the k arms with the largest means by taking as few samples as possible. In this paper, we make progress towards a complete characterization of the instance-wise sample complexity bounds for the Best-k-Arm problem. On the lower bound side, we obtain a novel complexity term to measure the sample complexity that every Best-k-Arm instance requires. This is derived by an interesting and nontrivial reduction from the Best-1-Arm problem. We also provide an elimination-based algorithm that matches the instance-wise lower bound within doubly-logarithmic factors. The sample complexity of our algorithm strictly dominates the state-of-the-art for Best-k-Arm (module constant factors).} }
Endnote
%0 Conference Paper %T Nearly Instance Optimal Sample Complexity Bounds for Top-k Arm Selection %A Lijie Chen %A Jian Li %A Mingda Qiao %B Proceedings of the 20th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2017 %E Aarti Singh %E Jerry Zhu %F pmlr-v54-chen17a %I PMLR %P 101--110 %U https://proceedings.mlr.press/v54/chen17a.html %V 54 %X In the Best-k-Arm problem, we are given n stochastic bandit arms, each associated with an unknown reward distribution. We are required to identify the k arms with the largest means by taking as few samples as possible. In this paper, we make progress towards a complete characterization of the instance-wise sample complexity bounds for the Best-k-Arm problem. On the lower bound side, we obtain a novel complexity term to measure the sample complexity that every Best-k-Arm instance requires. This is derived by an interesting and nontrivial reduction from the Best-1-Arm problem. We also provide an elimination-based algorithm that matches the instance-wise lower bound within doubly-logarithmic factors. The sample complexity of our algorithm strictly dominates the state-of-the-art for Best-k-Arm (module constant factors).
APA
Chen, L., Li, J. & Qiao, M.. (2017). Nearly Instance Optimal Sample Complexity Bounds for Top-k Arm Selection. Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 54:101-110 Available from https://proceedings.mlr.press/v54/chen17a.html.

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