Near-Optimal Regret Bounds for UCB-Style Gaussian Process Bandits via Data Thinning
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
The Flow has not summarised this story yet — read it at arXiv Machine Learning.
arXiv:2512. 00517v3 Announce Type: replace-cross Abstract: Sequential optimization of black-box functions from noisy evaluations has been widely studied, with Gaussian Process bandit algorithms such as GP-UCB guaranteeing no-regret in stationary settings.
arXiv:2608. 16492v1 Announce Type: cross Abstract: This paper studies the regret analysis for parallel Gaussian process (GP) bandit optimization.
The paper analyzes Bayesian linear bandits with isotropic Gaussian parameters, independent Gaussian arms, and Gaussian reward noise when the time horizon scales with the dimension. It derives explicit limits for the normalized posterior uncertainty and parameter overlaps, yielding exact regret curves for several policies—including Thompson sampling, posterior‑mean greedy selection, and scaled‑covariance variants. The results show that posterior‑mean greedy selection achieves the optimal Bayes regret, while Thompson sampling incurs a strictly larger leading regret whose ratio to greedy lies between one and two, approaching two for long horizons.
arXiv:2502. 01226v4 Announce Type: replace Abstract: Gaussian process (GP) bandits provide a powerful framework for performing blackbox optimization of unknown functions.
arXiv:2608. 18863v1 Announce Type: cross Abstract: We study Bayesian optimization in a time-varying environment where the unknown reward function evolves according to a Gaussian process drift model.
arXiv:2606. 28616v1 Announce Type: new Abstract: In stochastic linear bandits, the canonical Upper Confidence Bound (UCB) algorithm admits a simple frequentist regret analysis but can be computationally demanding, while Thompson Sampling (TS) is computationally attractive yet typically harder to analyze due to its non-optimistic nature.