Exploration scavenging

We examine the problem of evaluating a policy in the contextual bandit setting using only observations collected during the execution of another policy. We show that policy evaluation can be impossible if the exploration policy chooses actions based on the side information provided at each time step. We then propose and prove the correctness of a principled method for policy evaluation which works when this is not the case, even when the exploration policy is deterministic, as long as each action is explored sufficiently often. We apply this general technique to the problem of offline evaluation of internet advertising policies. Although our theoretical results hold only when the exploration policy chooses ads independent of side information, an assumption that is typically violated by commercial systems, we show how clever uses of the theory provide non-trivial and realistic applications. We also provide an empirical demonstration of the effectiveness of our techniques on real ad placement data.