English

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

Machine Learning 2020-10-07 v4 Machine Learning

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.

Keywords

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}
}
R2 v1 2026-06-23T09:21:33.993Z