#### Authors

Alex Strehl, John Langford, Lihong Li, Sham M. Kakade

#### Abstract

We provide a sound and consistent foundation for the use of \emph{nonrandom} exploration data in contextual bandit'' orpartially labeled'' settings where only the value of a chosen action is learned. The primary challenge in a variety of settings is that the exploration policy, in which offline'' data is logged, is not explicitly known. Prior solutions here require either control of the actions during the learning process, recorded random exploration, or actions chosen obliviously in a repeated manner. The techniques reported here lift these restrictions, allowing the learning of a policy for choosing actions given features from historical data where no randomization occurred or was logged. We empirically verify our solution on two reasonably sized sets of real-world data obtained from an Internet %online advertising company.