## Abstract

Contextual bandit learning is a reinforcement learning problem where the learner repeatedly receives a set of features (context), takes an action and receives a reward based on the action and context. We consider this problem under a realizability assumption: there exists a function in a (known) function class, always capable of predicting the expected reward, given the action and context. Under this assumption, we show three things. We present a new algorithm-Regressor Elimination-with a regret similar to the agnostic setting (i.e. in the absence of realizability assumption). We prove a new lower bound showing no algorithm can achieve superior performance in the worst case even with the realizability assumption. However, we do show that for any set of policies (mapping contexts to actions), there is a distribution over rewards (given context) such that our new algorithm has constant regret unlike the previous approaches.

Original language | English (US) |
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Pages (from-to) | 19-26 |

Number of pages | 8 |

Journal | Journal of Machine Learning Research |

Volume | 22 |

State | Published - 2012 |

Event | 15th International Conference on Artificial Intelligence and Statistics, AISTATS 2012 - La Palma, Spain Duration: Apr 21 2012 → Apr 23 2012 |

## All Science Journal Classification (ASJC) codes

- Software
- Artificial Intelligence
- Control and Systems Engineering
- Statistics and Probability