Improved Regret Bounds for Oracle-Based Adversarial Contextual Bandits

We give an oracle-based algorithm for the adversarial contextual bandit problem, where either contexts are drawn i.i.d. or the sequence of contexts is known a priori, but where the losses are picked adversarially. Our algorithm is computationally efficient, assuming access to an offline optimization oracle, and enjoys a regret of order O((KT)^frac23(log N)^frac13), where K is the number of actions, T is the number of iterations and N is the number of baseline policies. Our result is the first to break the O(T^frac34) barrier that is achieved by recently introduced algorithms. Breaking this barrier was left as a major open problem. Our analysis is based on the recent relaxation based approach of (Rakhlin and Sridharan, 2016).