OSOM: A simultaneously optimal algorithm for multi-armed and linear contextual bandits
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 the 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
@article{arxiv.1905.10040,
title = {OSOM: A simultaneously optimal algorithm for multi-armed and linear contextual bandits},
author = {Niladri S. Chatterji and Vidya Muthukumar and Peter L. Bartlett},
journal= {arXiv preprint arXiv:1905.10040},
year = {2020}
}