Acquisition for Spherical-Linear Bayesian Optimization on the Cube
Abstract
Recent work demonstrated that executing Bayesian Optimization (BO) using simply a linear surrogate with a clever transformation is enough to approximate the performance of the standard Gaussian-Process (GP) based version on high-dimensional test functions. When the decision region is a sphere, this strategy admits rapid exact acquisition. However, it is the unit cube we encounter most often in the BO literature, and in this setting a standard approach, namely a multi-start quasi-Newton method, is employed for solving the acquisition subproblem. In this article, we will discuss a series of results, both positive and negative, regarding the complexity of global resolution of various acquisition subproblems over the unit cube. On the basis of this discussion, we will propose a new acquisition function which is globally optimizable using significantly less execution time than the incumbent approach while maintaining or improving performance. The resulting method is competitive with GP-based BO in terms of accuracy per evaluation, and is superior in terms of accuracy per walltime on black-boxes of low to moderate computational intensity.
Related
- Simple Extensions of Single-Objective Acquisition Functions and Hedge Strategies for Multi-Objective Bayesian Optimization
- Multiplicity one for a linear spherical pair and its unitary analogue
- A Unified Optimism-Agnostic Framework for Linear Bandits over Spherical Action Sets
- TAP Accuracy Below the Fluctuation Scale and Universal Posterior Geometry in Spherical Linear Models
- Transfer learning in bayesian optimization for aircraft design
BibTeX
@misc{wycoff2026acquisition,
title = {{Acquisition for Spherical-Linear Bayesian Optimization on the Cube}},
author = {Nathan Wycoff},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32628},
eprint = {2610.32628},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32628},
}
RIS
TY - UNPB
TI - Acquisition for Spherical-Linear Bayesian Optimization on the Cube
AU - Nathan Wycoff
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32628
UR - https://arxiv.org/abs/2610.32628
AB - Recent work demonstrated that executing Bayesian Optimization (BO) using simply a linear surrogate with a clever transformation is enough to approximate the performance of the standard Gaussian-Process (GP) based version on high-dimensional test functions. When the decision region is a sphere, this strategy admits rapid exact acquisition. However, it is the unit cube we encounter most often in the BO literature, and in this setting a standard approach, namely a multi-start quasi-Newton method, is employed for solving the acquisition subproblem. In this article, we will discuss a series of results, both positive and negative, regarding the complexity of global resolution of various acquisition subproblems over the unit cube. On the basis of this discussion, we will propose a new acquisition function which is globally optimizable using significantly less execution time than the incumbent approach while maintaining or improving performance. The resulting method is competitive with GP-based BO in terms of accuracy per evaluation, and is superior in terms of accuracy per walltime on black-boxes of low to moderate computational intensity.
ER -