New theoretical research published on arXiv integrates the Gaussian-process upper confidence bound (GP-UCB) and decision-estimation-coefficient (DEC) methodologies within a unified algorithmic-information framework applicable to frequentist Reproducing Kernel Hilbert Space (RKHS) bandits1. This work bridges what were previously considered separate theoretical constructs by presenting them through a common computational language. Specifically, the paper highlights that GP-UCB operates by employing an algorithmic Gaussian-process prior instead of a true one, capitalizing on the complexity of observed data trajectories. By establishing this shared theoretical foundation, the research provides a deeper understanding of the inherent algorithmic and minimax complexities present in kernel bandit problems. This integration could facilitate advancements in designing more efficient and theoretically sound learning algorithms in complex decision-making environments. For practitioners, this foundational work offers critical insights into optimizing active learning and recommendation systems where balancing exploration and exploitation is paramount, potentially leading to more robust and performant models in real-world applications.