Gaussian-process upper confidence bound (GP-UCB) and decision-estimation-coefficient (DEC) methods may appear, at first sight, to belong to different theories. This paper places the two viewpoints in a common algorithmic-information language for frequentist RKHS bandits. GP-UCB fixes an algorithmic, rather than true, Gaussian-process prior and exploits realized-trajectory complexity together with computational tractability, whereas MAMS optimizes a robust class-wide MAIR/DEC envelope. Through the unified MAIR framework and heterogeneous positive-semidefinite algorithmic priors, we generalize both the GP-UCB analysis and the MAMS algorithm, propose a safeguarded master that combines their advantages, and provide a kernel-bandit construction showing that algorithmic complexity can be more informative than class-wide minimax or DEC certificates in overparameterized models. The resulting message is that algorithmic information and class-wide minimax coefficients answer different questions and can lead to different gaps; kernel bandits provide a clean setting in which this distinction becomes mathematically visible.

翻译：高斯过程上置信界（GP-UCB）与决策估计系数（DEC）方法乍看之下似乎属于不同理论体系。本文以频率学派再生核希尔伯特空间（RKHS）Bandits为背景，将这两种视角置于统一的算法信息语言框架下。GP-UCB固定了一个算法性（而非真实）高斯过程先验，并利用实现轨迹复杂度与计算可处理性相结合；而MAMS则优化一个稳健的类全局MAIR/DEC包络。通过统一的MAIR框架与异质半正定算法先验，我们推广了GP-UCB分析与MAMS算法，提出一种结合两者优势的稳健主算法，并给出一个核函数Bandits构造，表明在过参数化模型中算法复杂度可能比类全局极小极大或DEC证书更具信息量。本文由此传达的核心信息是：算法信息与类全局极小极大系数回答的是不同问题，并可能导致不同差距；核函数Bandits提供了一个清晰场景，使得这一区别在数学上变得直观可见。