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arXiv · 2508.18423

Enhancing Trust-Region Bayesian Optimization via Newton Methods

Quanlin Chen·Yiyu Chen·Jing Huo·Tianyu Ding·Yang Gao·Yuetong Chen
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Abstract

Bayesian Optimization (BO) has been widely applied to optimize expensive black-box functions while retaining sample efficiency. However, scaling BO to high-dimensional spaces remains challenging. Existing literature proposes performing standard BO in multiple local trust regions (TuRBO) for heterogeneous modeling of the objective function and avoiding over-exploration. Despite its advantages, using local Gaussian Processes (GPs) reduces sampling efficiency compared to a global GP. To enhance sampling efficiency while preserving heterogeneous modeling, we propose to construct multiple local quadratic models using gradients and Hessians from a global GP, and select new sample points by solving the bound-constrained quadratic program. Additionally, we address the issue of vanishing gradients of GPs in high-dimensional spaces. We provide a convergence analysis and demonstrate through experimental results that our method enhances the efficacy of TuRBO and outperforms a wide range of high-dimensional BO techniques on synthetic functions and real-world applications.

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Quanlin Chen, Yiyu Chen, Jing Huo, Tianyu Ding, Yang Gao, Yuetong Chen. 2025-08-25. Enhancing Trust-Region Bayesian Optimization via Newton Methods. https://arxiv.org/abs/2508.18423

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