OSOM: A simultaneously optimal algorithm for multi-armed and linear contextual bandits

Niladri Chatterji, Vidya Muthukumar, Peter Bartlett
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:1844-1854, 2020.

Abstract

We consider the stochastic linear (multi-armed) contextual bandit problem with the possibility of hidden simple multi-armed bandit structure in which the rewards are independent of the contextual information. Algorithms that are designed solely for one of the regimes are known to be sub-optimal for their alternate regime. We design a single computationally efficient algorithm that simultaneously obtains problem-dependent optimal regret rates in the simple multi-armed bandit regime and minimax optimal regret rates in the linear contextual bandit regime, without knowing a priori which of the two models generates the rewards. These results are proved under the condition of stochasticity of contextual information over multiple rounds. Our results should be viewed as a step towards principled data-dependent policy class selection for contextual bandits.

Cite this Paper

BibTeX
@InProceedings{pmlr-v108-chatterji20b, title = {OSOM: A simultaneously optimal algorithm for multi-armed and linear contextual bandits}, author = {Chatterji, Niladri and Muthukumar, Vidya and Bartlett, Peter}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {1844--1854}, year = {2020}, editor = {Chiappa, Silvia and Calandra, Roberto}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/chatterji20b/chatterji20b.pdf}, url = {https://proceedings.mlr.press/v108/chatterji20b.html}, abstract = {We consider the stochastic linear (multi-armed) contextual bandit problem with the possibility of hidden simple multi-armed bandit structure in which the rewards are independent of the contextual information. Algorithms that are designed solely for one of the regimes are known to be sub-optimal for their alternate regime. We design a single computationally efficient algorithm that simultaneously obtains problem-dependent optimal regret rates in the simple multi-armed bandit regime and minimax optimal regret rates in the linear contextual bandit regime, without knowing a priori which of the two models generates the rewards. These results are proved under the condition of stochasticity of contextual information over multiple rounds. Our results should be viewed as a step towards principled data-dependent policy class selection for contextual bandits.} }
Endnote
%0 Conference Paper %T OSOM: A simultaneously optimal algorithm for multi-armed and linear contextual bandits %A Niladri Chatterji %A Vidya Muthukumar %A Peter Bartlett %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-chatterji20b %I PMLR %P 1844--1854 %U https://proceedings.mlr.press/v108/chatterji20b.html %V 108 %X We consider the stochastic linear (multi-armed) contextual bandit problem with the possibility of hidden simple multi-armed bandit structure in which the rewards are independent of the contextual information. Algorithms that are designed solely for one of the regimes are known to be sub-optimal for their alternate regime. We design a single computationally efficient algorithm that simultaneously obtains problem-dependent optimal regret rates in the simple multi-armed bandit regime and minimax optimal regret rates in the linear contextual bandit regime, without knowing a priori which of the two models generates the rewards. These results are proved under the condition of stochasticity of contextual information over multiple rounds. Our results should be viewed as a step towards principled data-dependent policy class selection for contextual bandits.
APA
Chatterji, N., Muthukumar, V. & Bartlett, P.. (2020). OSOM: A simultaneously optimal algorithm for multi-armed and linear contextual bandits. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:1844-1854 Available from https://proceedings.mlr.press/v108/chatterji20b.html.

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