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Bypassing the Monster: A Faster and Simpler Optimal Algorithm for Contextual Bandits Under Realizability

Author

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  • David Simchi-Levi

    (Institute for Data, Systems, and Society, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139; Department of Civil and Environmental Engineering and Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Yunzong Xu

    (Institute for Data, Systems, and Society, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139; Statistics and Data Science Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

Abstract

We consider the general (stochastic) contextual bandit problem under the realizability assumption, that is, the expected reward, as a function of contexts and actions, belongs to a general function class F . We design a fast and simple algorithm that achieves the statistically optimal regret with only O ( log T ) calls to an offline regression oracle across all T rounds. The number of oracle calls can be further reduced to O ( log log T ) if T is known in advance. Our results provide the first universal and optimal reduction from contextual bandits to offline regression, solving an important open problem in the contextual bandit literature. A direct consequence of our results is that any advances in offline regression immediately translate to contextual bandits, statistically and computationally. This leads to faster algorithms and improved regret guarantees for broader classes of contextual bandit problems.

Suggested Citation

  • David Simchi-Levi & Yunzong Xu, 2022. "Bypassing the Monster: A Faster and Simpler Optimal Algorithm for Contextual Bandits Under Realizability," Mathematics of Operations Research, INFORMS, vol. 47(3), pages 1904-1931, August.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:3:p:1904-1931
    DOI: 10.1287/moor.2021.1193
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