TY  - EJOUR
AU  - Georgiou, Anastasia
AU  - Jungen, Daniel
AU  - Kaven, Luise
AU  - Hunstig, Verena
AU  - Frangakis, Constantine
AU  - Kevrekidis, Ioannis
AU  - Mitsos, Alexander
TI  - Deterministic Global Optimization of the Acquisition Function in Bayesian Optimization: To Do or Not To Do?
PB  - arXiv
M1  - FZJ-2025-03099
PY  - 2025
AB  - Bayesian Optimization (BO) with Gaussian Processes relies on optimizing an acquisition function to determine sampling. We investigate the advantages and disadvantages of using a deterministic global solver (MAiNGO) compared to conventional local and stochastic global solvers (L-BFGS-B and multi-start, respectively) for the optimization of the acquisition function. For CPU efficiency, we set a time limit for MAiNGO, taking the best point as optimal. We perform repeated numerical experiments, initially using the Muller-Brown potential as a benchmark function, utilizing the lower confidence bound acquisition function; we further validate our findings with three alternative benchmark functions. Statistical analysis reveals that when the acquisition function is more exploitative (as opposed to exploratory), BO with MAiNGO converges in fewer iterations than with the local solvers. However, when the dataset lacks diversity, or when the acquisition function is overly exploitative, BO with MAiNGO, compared to the local solvers, is more likely to converge to a local rather than a global ly near-optimal solution of the black-box function. L-BFGS-B and multi-start mitigate this risk in BO by introducing stochasticity in the selection of the next sampling point, which enhances the exploration of uncharted regions in the search space and reduces dependence on acquisition function hyperparameters. Ultimately, suboptimal optimization of poorly chosen acquisition functions may be preferable to their optimal solution. When the acquisition function is more exploratory, BO with MAiNGO, multi-start, and L-BFGS-B achieve comparable probabilities of convergence to a globally near-optimal solution (although BO with MAiNGO may require more iterations to converge under these conditions).
KW  - Optimization and Control (math.OC) (Other)
KW  - Machine Learning (cs.LG) (Other)
KW  - FOS: Mathematics (Other)
KW  - FOS: Computer and information sciences (Other)
LB  - PUB:(DE-HGF)25
DO  - DOI:10.48550/ARXIV.2503.03625
UR  - https://juser.fz-juelich.de/record/1044210
ER  -