aiqbench analysis
This paper unifies GP-UCB and MAMS methodologies within a common algorithmic-information framework for frequentist RKHS bandits, demonstrating that algorithmic complexity can offer more informative bounds than class-wide minimax certificates in overparameterized models. By proposing a safeguarded master algorithm that combines these approaches, the work clarifies how algorithmic information and minimax coefficients address distinct theoretical questions with potentially divergent performance gaps. The study establishes kernel bandits as a rigorous setting where this mathematical distinction becomes visible, advancing the theoretical foundations of reinforcement learning and optimization.
Algorithmic and Minimax Complexities in Kernel Bandits
arXiv:2606.11171v1 Announce Type: new Abstract: 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.
Abstract: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.
Machine Learning (cs.LG); Statistical Mechanics (cond-mat.stat-mech); Information Theory (cs.IT); Optimization and Control (math.OC); Statistics Theory (math.ST)
arXiv:2606.11171 [cs.LG]
(or arXiv:2606.11171v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.11171 arXiv-issued DOI via DataCite (pending registration)
Full text under the publisher's open licence · 173 words
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