Near-Optimal Regret Bounds for UCB-Style Gaussian Process Bandits via Data Thinning

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.