An Improved Relaxation for Oracle-Efficient Adversarial Contextual Bandits

• URL: http://arxiv.org/abs/2310.19025v2
• Date: Fri, 10 Nov 2023 16:14:10 GMT
• Title: An Improved Relaxation for Oracle-Efficient Adversarial Contextual Bandits
• Authors: Kiarash Banihashem, MohammadTaghi Hajiaghayi, Suho Shin, Max Springer
• Abstract summary: We present an oracle-efficient relaxation for the adversarial contextual bandits problem. Our algorithm has a regret bound of $O(Tfrac23(Klog(|Pi|))frac13)$ and makes at most $O(K)$ calls per round to an offline optimization.
• Score: 14.058574632553547
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present an oracle-efficient relaxation for the adversarial contextual bandits problem, where the contexts are sequentially drawn i.i.d from a known distribution and the cost sequence is chosen by an online adversary. Our algorithm has a regret bound of $O(T^{\frac{2}{3}}(K\log(|\Pi|))^{\frac{1}{3}})$ and makes at most $O(K)$ calls per round to an offline optimization oracle, where $K$ denotes the number of actions, $T$ denotes the number of rounds and $\Pi$ denotes the set of policies. This is the first result to improve the prior best bound of $O((TK)^{\frac{2}{3}}(\log(|\Pi|))^{\frac{1}{3}})$ as obtained by Syrgkanis et al. at NeurIPS 2016, and the first to match the original bound of Langford and Zhang at NeurIPS 2007 which was obtained for the stochastic case.

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