001044210 001__ 1044210
001044210 005__ 20250717202256.0
001044210 0247_ $$2doi$$a10.48550/ARXIV.2503.03625
001044210 037__ $$aFZJ-2025-03099
001044210 1001_ $$0P:(DE-HGF)0$$aGeorgiou, Anastasia$$b0
001044210 245__ $$aDeterministic Global Optimization of the Acquisition Function in Bayesian Optimization: To Do or Not To Do?
001044210 260__ $$barXiv$$c2025
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001044210 520__ $$aBayesian 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).
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001044210 650_7 $$2Other$$aOptimization and Control (math.OC)
001044210 650_7 $$2Other$$aMachine Learning (cs.LG)
001044210 650_7 $$2Other$$aFOS: Mathematics
001044210 650_7 $$2Other$$aFOS: Computer and information sciences
001044210 7001_ $$0P:(DE-HGF)0$$aJungen, Daniel$$b1
001044210 7001_ $$0P:(DE-HGF)0$$aKaven, Luise$$b2
001044210 7001_ $$0P:(DE-HGF)0$$aHunstig, Verena$$b3
001044210 7001_ $$0P:(DE-HGF)0$$aFrangakis, Constantine$$b4
001044210 7001_ $$0P:(DE-HGF)0$$aKevrekidis, Ioannis$$b5
001044210 7001_ $$0P:(DE-Juel1)172025$$aMitsos, Alexander$$b6$$eCorresponding author$$ufzj
001044210 773__ $$a10.48550/ARXIV.2503.03625
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001044210 9101_ $$0I:(DE-HGF)0$$6P:(DE-HGF)0$$a Johns Hopkins University$$b0
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001044210 9101_ $$0I:(DE-HGF)0$$6P:(DE-HGF)0$$a Johns Hopkins University$$b5
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