Unified Framework Reconciles Algorithmic and Minimax Complexity in Kernel Bandits
Researchers have developed a unified mathematical framework that reconciles two previously distinct theoretical approaches to kernel bandits: Gaussian-process upper confidence bound (GP-UCB) methods and decision-estimation-coefficient (DEC) approaches. The work demonstrates that algorithmic complexity and class-wide minimax coefficients answer fundamentally different questions and can produce different performance gaps in overparameterized models. This theoretical advance clarifies how different complexity measures relate to each other and provides a safeguarded algorithm combining advantages of both approaches.
A new paper on arXiv presents a unified algorithmic-information framework for analyzing kernel bandits, a fundamental problem in online learning and optimization. The authors show that GP-UCB methods, which fix an algorithmic Gaussian-process prior and exploit realized-trajectory complexity, and MAMS algorithms, which optimize robust class-wide decision-estimation-coefficient envelopes, can be understood within a common mathematical language using heterogeneous positive-semidefinite algorithmic priors. The work generalizes both existing analyses and proposes a safeguarded master algorithm that combines their respective advantages. A key contribution is demonstrating through kernel-bandit constructions that algorithmic complexity can be more informative than class-wide minimax or DEC certificates in overparameterized settings. The authors argue that this distinction becomes mathematically visible in kernel bandits, providing a clean theoretical setting for understanding when different complexity measures diverge.
What's missing
The paper does not discuss empirical validation or experimental results comparing the proposed safeguarded master algorithm against existing methods on benchmark problems. Additionally, practical implications for real-world applications of kernel bandits are not addressed.
What different sources said
- arXiv cs.LGCenter
Algorithmic and Minimax Complexities in Kernel Bandits
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