NeST-BO: Fast Local Bayesian Optimization via Newton-Step Targeting of Gradient and Hessian Information

Wei-Ting Tang, Akshay Kudva, Joel Paulson
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:1882-1890, 2026.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-tang26c, title = { NeST-BO: Fast Local Bayesian Optimization via Newton-Step Targeting of Gradient and Hessian Information }, author = {Tang, Wei-Ting and Kudva, Akshay and Paulson, Joel}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {1882--1890}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/tang26c/tang26c.pdf}, url = {https://proceedings.mlr.press/v300/tang26c.html}, abstract = { 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. } }
Endnote
%0 Conference Paper %T NeST-BO: Fast Local Bayesian Optimization via Newton-Step Targeting of Gradient and Hessian Information %A Wei-Ting Tang %A Akshay Kudva %A Joel Paulson %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-tang26c %I PMLR %P 1882--1890 %U https://proceedings.mlr.press/v300/tang26c.html %V 300 %X 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.
APA
Tang, W., Kudva, A. & Paulson, J.. (2026). NeST-BO: Fast Local Bayesian Optimization via Newton-Step Targeting of Gradient and Hessian Information . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:1882-1890 Available from https://proceedings.mlr.press/v300/tang26c.html.

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