NeST-BO: Fast Local Bayesian Optimization via Newton-Step Targeting of Gradient and Hessian Information
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arXiv
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| Format: | Preprint |
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2025
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| author | Tang, Wei-Ting Kudva, Akshay Paulson, Joel A. |
| author_facet | Tang, Wei-Ting Kudva, Akshay Paulson, Joel A. |
| contents | Bayesian optimization (BO) is effective for expensive black-box problems but remains challenging in high dimensions. We propose NeST-BO, a curvature-aware local BO method that targets a (modified) Newton step by jointly learning gradient and Hessian information with Gaussian process (GP) surrogates, and selecting evaluations via a one-step lookahead bound on the Newton-step error. We show that this bound contracts with batch size, so NeST-BO drives the step error to zero; in well-behaved neighborhoods it recovers the fast local convergence behavior of inexact/modified Newton methods, while standard safeguards support global convergence to stationary points. To improve scaling with problem dimension, we optimize the acquisition in low-dimensional embedded subspaces (random or learned), reducing the dominant cost of learning curvature from $O(d^2)$ to $O(m^2)$ with $m \ll d$ while preserving step targeting. Across high-dimensional synthetic and real-world problems, including cases with thousands of variables and unknown active subspaces, NeST-BO consistently yields faster convergence and better final values than state-of-the-art local and high-dimensional BO baselines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05516 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | NeST-BO: Fast Local Bayesian Optimization via Newton-Step Targeting of Gradient and Hessian Information Tang, Wei-Ting Kudva, Akshay Paulson, Joel A. Machine Learning Optimization and Control Bayesian optimization (BO) is effective for expensive black-box problems but remains challenging in high dimensions. We propose NeST-BO, a curvature-aware local BO method that targets a (modified) Newton step by jointly learning gradient and Hessian information with Gaussian process (GP) surrogates, and selecting evaluations via a one-step lookahead bound on the Newton-step error. We show that this bound contracts with batch size, so NeST-BO drives the step error to zero; in well-behaved neighborhoods it recovers the fast local convergence behavior of inexact/modified Newton methods, while standard safeguards support global convergence to stationary points. To improve scaling with problem dimension, we optimize the acquisition in low-dimensional embedded subspaces (random or learned), reducing the dominant cost of learning curvature from $O(d^2)$ to $O(m^2)$ with $m \ll d$ while preserving step targeting. Across high-dimensional synthetic and real-world problems, including cases with thousands of variables and unknown active subspaces, NeST-BO consistently yields faster convergence and better final values than state-of-the-art local and high-dimensional BO baselines. |
| title | NeST-BO: Fast Local Bayesian Optimization via Newton-Step Targeting of Gradient and Hessian Information |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2510.05516 |