Improved regret bounds for oracle-based adversarial contextual bandits

We propose a new oracle-based algorithm, BISTRO+, 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 achieved by recent algorithms, which was left as a major open problem. Our analysis employs the recent relaxation framework of Rakhlin and Sridharan [7].