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

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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.

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