Unified Framework Reconciles Algorithmic and Minimax Complexity in Kernel Bandits
Researchers have proposed a unified theoretical framework called MAIR that bridges two previously distinct approaches to kernel bandit optimization: GP-UCB and decision-estimation-coefficient (DEC) methods. The paper demonstrates that algorithmic complexity and class-wide minimax coefficients answer fundamentally different questions, with kernel bandits serving as a clean mathematical setting to expose this distinction. The work matters because it offers a more nuanced understanding of when each approach is more informative, particularly in overparameterized models.
A preprint submitted to arXiv on June 9, 2026 introduces the MAIR (Minimax Algorithmic Information Regret) framework, which places GP-UCB and DEC-based methods within a common algorithmic-information language for frequentist RKHS bandits. GP-UCB is characterized as fixing an algorithmic Gaussian-process prior and exploiting realized-trajectory complexity, while the MAMS algorithm optimizes a robust class-wide MAIR/DEC envelope. Using heterogeneous positive-semidefinite algorithmic priors, the authors generalize both approaches and propose a 'safeguarded master' algorithm that combines their respective advantages. A key theoretical contribution is a kernel-bandit construction demonstrating that algorithmic complexity can be strictly more informative than class-wide minimax or DEC certificates in overparameterized settings. The paper concludes that the two paradigms are complementary rather than competing, and that their differences become mathematically visible in the kernel bandit setting.
What's missing
As a preprint, this work has not yet undergone peer review, so its theoretical claims and proofs have not been independently verified. The paper does not appear to include empirical experiments validating the practical performance of the proposed safeguarded master algorithm, leaving open questions about real-world applicability and computational overhead relative to existing methods.
What different sources said
- arXiv cs.LGCenter
Algorithmic and Minimax Complexities in Kernel Bandits
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