We study a generalization of the problem of online learning in adversarial linear contextual bandits by incorporating loss functions that belong to a reproducing kernel Hilbert space, which allows for a more flexible modeling of complex decision-making scenarios. We propose a computationally efficient algorithm that makes use of a new optimistically biased estimator for the loss functions and achieves near-optimal regret guarantees under a variety of eigenvalue decay assumptions made on the underlying kernel. Specifically, under the assumption of polynomial eigendecay with exponent $c>1$, the regret is $\widetilde{O}(KT^{\frac{1}{2}(1+\frac{1}{c})})$, where $T$ denotes the number of rounds and $K$ the number of actions. Furthermore, when the eigendecay follows an exponential pattern, we achieve an even tighter regret bound of $\widetilde{O}(\sqrt{T})$. These rates match the lower bounds in all special cases where lower bounds are known at all, and match the best known upper bounds available for the more well-studied stochastic counterpart of our problem.

通过将属于再现核希尔伯特空间的损失函数纳入到对手性线性背景乐队的在线学习问题的研究中，我们提出了一种计算有效的算法，该算法利用一种新的对损失函数进行乐观偏差估计的方法，在对底层内核进行的各种特征值衰减假设下实现接近最佳的后悔保证。

对抗语境强化学习的核化方法