arXiv：cs.LG· Shion Takeno·· 4 小时前AI 评分33
一步前瞻贝叶斯优化的遗憾界研究：OVR 方法
Towards Regret Guarantees for One-Step Lookahead Bayesian Optimization
AI 导读
这篇论文分析了名为 optimal-point variance reduction（OVR）的一步前瞻贝叶斯优化方法，该方法仅需后验采样和蒙特卡洛近似。作者给出了采集函数计算中输入域上一致的蒙特卡洛估计误差界，并证明经正则化（便于探索）后的 OVR 可实现趋于零的贝叶斯期望简单遗憾上界。数值实验验证了 OVR 与正则化 OVR 的性能。
正文
Abstract:This paper studies theoretical guarantees of a one-step lookahead Bayesian optimization (BO) method. Although the empirical effectiveness of one-step lookahead BO methods, such as entropy search, has been studied extensively, they often rely on computationally intractable approximations, and their regret guarantees remain underdeveloped. Thus, this paper analyzes a one-step lookahead BO method, which we refer to as optimal-point variance reduction (OVR), that requires only posterior sampling and Monte Carlo approximations. We obtain a uniform Monte Carlo estimation error bound over an input domain in an acquisition function computation. Furthermore, we show that the regularized OVR, with a slight modification to facilitate exploration, achieves a vanishing Bayesian expected simple regret upper bound. Finally, we validate the performance of OVR and regularized OVR through numerical experiments.
| Comments: | 27pages, 4 figures |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2606.00956 [cs.LG] |
| (or arXiv:2606.00956v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.00956 arXiv-issued DOI via DataCite |
Submission history
From: Shion Takeno [view email]
[v1]
Sun, 31 May 2026 02:16:21 UTC (388 KB)
[v2]
Wed, 7 Oct 2026 11:27:48 UTC (745 KB)
来源：arXiv：cs.LG · arxiv.org