[Submitted on 26 Feb 2025 (v1), last revised 30 Oct 2026 (this version, v3)]
Abstract:We study the noise-free Gaussian Process (GP) bandits problem, in which the learner seeks to minimize regret through noise-free observations of the black-box objective function lying on the known reproducing kernel Hilbert space (RKHS). Gaussian process upper confidence bound (GP-UCB) is the well-known GP-bandits algorithm whose query points are adaptively chosen based on the GP-based upper confidence bound score. Although several existing works have reported the practical success of GP-UCB, the current theoretical results indicate its suboptimal performance. However, GP-UCB tends to perform well empirically compared with other nearly optimal noise-free algorithms that rely on a non-adaptive sampling scheme of query points. This paper resolves this gap between theoretical and empirical performance by showing the nearly optimal regret upper bound of noise-free GP-UCB. Specifically, our analysis shows the first constant cumulative regret in the noise-free settings for the squared exponential kernel and Matérn kernel with some degree of smoothness.
Submission history
From: Shogo Iwazaki [view email]
[v1] Wed, 26 Feb 2025 10:10:51 UTC (24 KB)
[v2] Wed, 10 Dec 2025 22:27:16 UTC (93 KB)
[v3] Fri, 30 Oct 2026 09:38:22 UTC (90 KB)
