Enhancing Trust-Region Bayesian Optimization via Derivatives of Gaussian Processes

Quanlin Chen, Yiyu Chen, Jing Huo, Tianyu Ding, Yang Gao, Yuetong Chen

Keywords: Bayesian optimization, High-dimensional Bayesian optimization, Trust-Region methods

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 several 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 several local quadratic models using gradients and Hessians from a global GP, and select new sample points by solving the bound-constrained quadratic program. 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.

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

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Submission Number: 13989