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arXiv · 2310.19025

An Improved Relaxation for Oracle-Efficient Adversarial Contextual Bandits

Kiarash Banihashem·MohammadTaghi Hajiaghayi·Suho Shin·Max Springer
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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 $O(T^{\frac{2}{3}}(K\log(|Π|))^{\frac{1}{3}})$ 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 $Π$ denotes the set of policies. This is the first result to improve the prior best bound of $O((TK)^{\frac{2}{3}}(\log(|Π|))^{\frac{1}{3}})$ 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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Kiarash Banihashem, MohammadTaghi Hajiaghayi, Suho Shin, Max Springer. 2023-11-10. An Improved Relaxation for Oracle-Efficient Adversarial Contextual Bandits. https://arxiv.org/abs/2310.19025

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