OSOM: A simultaneously optimal algorithm for multi-armed and linear contextual bandits
Niladri Chatterji, Vidya Muthukumar, Peter Bartlett
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.
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.}
}