Acquisition for Spherical-Linear Bayesian Optimization on the Cube

TL;DR

This paper introduces a novel acquisition function for spherical-linear Bayesian optimization on the unit cube, enabling globally optimal acquisition with significantly reduced computation time compared to multi-start quasi-Newton methods. The approach maintains competitive accuracy per evaluation and outperforms standard GP-based BO in accuracy per walltime for low-to-moderate cost black-box functions.

Why It Matters

Efficient acquisition optimization is critical for scaling Bayesian optimization to high-dimensional problems. By enabling faster, globally optimal acquisition on the unit cube—common in real-world applications—the method improves practical deployment speed without sacrificing accuracy, especially beneficial for computationally expensive or moderately intensive black-box optimization tasks.

Key Findings

• Spherical-linear surrogates enable exact acquisition on spherical domains but face challenges on the unit cube.
• Standard multi-start quasi-Newton methods for acquisition are computationally expensive and not globally optimal.
• The proposed acquisition function achieves global optimality with much lower runtime while preserving or improving optimization performance.