New Algorithms for Adaptive Prior Selection in Gaussian Process Bandits
Researchers have proposed two algorithms — PE-GP-TS and HP-GP-TS — that jointly handle prior selection and regret minimization in Gaussian process bandit optimization. Most existing work assumes the GP prior is known in advance, but in practice it rarely is, and the common workaround of maximum likelihood estimation lacks theoretical guarantees. The work is significant because HP-GP-TS comes with a provable sublinear regret bound, offering a theoretically grounded alternative for black-box optimization under prior uncertainty.
Gaussian process (GP) bandits are a widely used framework for black-box optimization of unknown functions, but their performance depends critically on the choice of GP prior. In practice, the true prior is rarely known, and practitioners typically resort to maximum likelihood estimation for hyperparameter selection — an approach that lacks formal theoretical backing. To address this gap, researchers Jack Sandberg and collaborators introduce two Thompson sampling-based algorithms: Prior-Elimination GP-TS (PE-GP-TS), which progressively discards priors with poor predictive performance, and HyperPrior GP-TS (HP-GP-TS), which employs a bi-level Thompson sampling scheme to simultaneously learn the prior and minimize regret. The paper provides a theoretical analysis establishing a sublinear regret bound for HP-GP-TS, a meaningful guarantee absent from prior approaches. Extensive experiments on both synthetic and real-world datasets demonstrate that the proposed methods outperform existing alternatives. The preprint, spanning 30 pages and 12 figures, has undergone four revisions on arXiv between February 2025 and June 2026, suggesting ongoing refinement.
What's missing
The paper does not yet appear to have undergone formal peer review at a named venue, so independent validation of the theoretical claims and experimental results is pending. Key open questions include how the algorithms scale with very large prior candidate sets, whether the sublinear regret bound for HP-GP-TS is tight, and how PE-GP-TS performs theoretically (no regret bound is established for it).
What different sources said
- arXiv cs.LGCenter
Adaptive Prior Selection in Gaussian Process Bandits with Thompson Sampling
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