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arXiv · 1606.00313

Improved Regret Bounds for Oracle-Based Adversarial Contextual Bandits

Vasilis Syrgkanis·Haipeng Luo·Akshay Krishnamurthy·Robert E. Schapire
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Abstract

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 $O((KT)^{\frac{2}{3}}(\log N)^{\frac{1}{3}})$, 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 $O(T^{\frac{3}{4}})$ 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, 2016).

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Vasilis Syrgkanis, Haipeng Luo, Akshay Krishnamurthy, Robert E. Schapire. 2016-06-01. Improved Regret Bounds for Oracle-Based Adversarial Contextual Bandits. https://arxiv.org/abs/1606.00313

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