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.

翻译：我们提出了一种针对对抗性上下文赌博机问题的预言机高效松弛方法，其上下文序列独立同分布于已知分布，而代价序列由在线对抗方选择。该算法的遗憾界为 $O(T^{\frac{2}{3}}(K\log(|\Pi|))^{\frac{1}{3}})$，且每轮对离线优化预言机的调用次数不超过 $O(K)$，其中 $K$ 表示动作数，$T$ 表示轮数，$\Pi$ 表示策略集。这是首个将先前 Syrgkanis 等人（NeurIPS 2016）得到的最优界 $O((TK)^{\frac{2}{3}}(\log(|\Pi|))^{\frac{1}{3}})$ 进行改进的结果，同时也是首个匹配 Langford 与 Zhang（NeurIPS 2007）针对随机情形得到的原始界的结果。