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 $O((KT )^{2/3} (log N)^{1/3})$, 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 $O(T^{3/4})$ 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 [7].