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Contextual Bandit Learning with Predictable Rewards

Author(s): Agarwal, Alekh; Dudík, Miroslav; Kale, Satyen; Langford, John; Schapire, Robert E

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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.
Publication Date: 2012
Citation: Agarwal, Alekh, Dudík, Miroslav, Kale, Satyen, Langford, John, Schapire, Robert E. (Contextual Bandit Learning with Predictable Rewards
Type of Material: Conference Article
Journal/Proceeding Title: 15th International Conference on Artificial Intelligence and Statistics (AISTATS) 2012
Version: Final published version. This is an open access article.

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