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This paper is a theoretical machine learning result: it proves regret bounds for Gaussian process bandit algorithms, using data thinning to get tighter confidence intervals and improve on the known suboptimal GP-UCB bound. The gains are asymptotic guarantees under a Gaussian noise assumption, and the numerical experiments are the only empirical check, so readers should treat the practical impact as unproven until others replicate it at scale. It is most relevant to researchers working on sequential decision-making, Bayesian optimization, and active learning.
Near-Optimal Regret Bounds for UCB-Style Gaussian Process Bandits via Data Thinning
arXiv:2610.28136v1 Announce Type: cross Abstract: Gaussian process upper confidence bound (GP-UCB) has been widely studied, though its known regret upper bound is suboptimal. To obtain near-optimal regret upper bounds, existing studies mainly focus on non-adaptive methods, such as uncertainty sampling, whose practical effectiveness is often limited. This paper shows that, under a Gaussian noise assumption, UCB-style algorithms can achieve near-optimal regret upper bounds via data thinning, a statistical technique for creating independent datasets from a single dataset. First, we show that data thinning can yield tighter confidence intervals in the bandit setting, and that a direct extension of GP-UCB achieves a near-optimal simple regret upper bound. Furthermore, by leveraging the tighter confidence intervals and combining GP-UCB with a phased elimination algorithm, we show a near-optimal cumulative regret upper bound. Finally, we demonstrate the effectiveness of UCB-style algorithms incorporating data thinning via numerical experiments.
Abstract:Gaussian process upper confidence bound (GP-UCB) has been widely studied, though its known regret upper bound is suboptimal. To obtain near-optimal regret upper bounds, existing studies mainly focus on non-adaptive methods, such as uncertainty sampling, whose practical effectiveness is often limited. This paper shows that, under a Gaussian noise assumption, UCB-style algorithms can achieve near-optimal regret upper bounds via data thinning, a statistical technique for creating independent datasets from a single dataset. First, we show that data thinning can yield tighter confidence intervals in the bandit setting, and that a direct extension of GP-UCB achieves a near-optimal simple regret upper bound. Furthermore, by leveraging the tighter confidence intervals and combining GP-UCB with a phased elimination algorithm, we show a near-optimal cumulative regret upper bound. Finally, we demonstrate the effectiveness of UCB-style algorithms incorporating data thinning via numerical experiments.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2610.28136 [stat.ML]
(or arXiv:2610.28136v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2610.28136 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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