Abstract
We consider online learning where there is access to a large, partially observable, offline dataset that was sampled from some fixed policy. For contextual bandits, we show that this problem is closely related to a variant of the bandit problem with side information. We construct a linear bandit algorithm that takes advantage of the projected information, and prove regret bounds. Our results demonstrate the ability to take full advantage of partially observable offline data. Particularly, we prove regret bounds that improve current bounds by a factor related to the visible dimensionality of the contexts in the data. Our results indicate that partially observable offline data can significantly improve online learning algorithms. We demonstrate various characteristics of our approach through synthetic simulations. Finally, we discuss the dynamic case where we present preliminary results for Markov decision processes.