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@ARTICLE{Georgiou:1044210,
      author       = {Georgiou, Anastasia and Jungen, Daniel and Kaven, Luise and
                      Hunstig, Verena and Frangakis, Constantine and Kevrekidis,
                      Ioannis and Mitsos, Alexander},
      title        = {{D}eterministic {G}lobal {O}ptimization of the
                      {A}cquisition {F}unction in {B}ayesian {O}ptimization: {T}o
                      {D}o or {N}ot {T}o {D}o?},
      publisher    = {arXiv},
      reportid     = {FZJ-2025-03099},
      year         = {2025},
      abstract     = {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).},
      keywords     = {Optimization and Control (math.OC) (Other) / Machine
                      Learning (cs.LG) (Other) / FOS: Mathematics (Other) / FOS:
                      Computer and information sciences (Other)},
      cin          = {ICE-1},
      cid          = {I:(DE-Juel1)ICE-1-20170217},
      pnm          = {899 - ohne Topic (POF4-899)},
      pid          = {G:(DE-HGF)POF4-899},
      typ          = {PUB:(DE-HGF)25},
      doi          = {10.48550/ARXIV.2503.03625},
      url          = {https://juser.fz-juelich.de/record/1044210},
}