(519g) Linking Bayesian Optimization with Deterministic Global Gaussian Process Optimization for Active Determination of Optimal Policies: From Catalysis to Cancer Treatment

Bayesian optimization (BO) has become a prominent method for optimizing expensive-to-evaluate black-box functions, relying on the construction of a surrogate model, typically a Gaussian Process (GP), to guide the search for global minima [1]. While BO has seen widespread adoption and implementation in various software packages, the optimization of the acquisition function, a crucial step in the BO loop, often employs local or stochastic global solvers such as multi-start limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS). This method may fail to locate the global minimum of the acquisition function and increase the overall number of iterations needed for BO to converge.

In this work, we explore the effects of using deterministic global optimization techniques for GP models (here, using MAiNGO/MeLOn [2, 3]) in place of traditional local solvers during optimization of the acquisition functions in BO. Specifically, we study its effects on a simple Müller-Brown potential illustration, and then proceed to studying its effects on a policy optimization for dynamic ammonia catalysis and a personalized cancer-chemotherapy treatment policy [3]. Our results highlight the potential of deterministic global optimization within BO to achieve more efficient optimization outcomes, particularly in scenarios where the acquisition function is characterized by complex landscapes with multiple minima.

[1] B Shahriari, K Swersky, Z Wang, RP Adams, and Nando de Freitas. Taking the human out of the loop: A review of bayesian optimization. Proceedings of the IEEE, 104(1):148–175, 2016.

[2] D Bongartz, J Najman, S Sass, and A Mitsos, MAiNGO - McCormick-based Algorithm for mixed-integer Nonlinear Global Optimization. Technical Report, Process Systems Engineering (AVT.SVT), RWTH Aachen University (2018).

[3] AM Schweidtmann, D Bongartz, D Grothe, T Kerkenhoff, X Lin, J Najman, and A Mitsos. Deterministic global optimization with gaussian processes embedded. Mathematical Programming Computation, 13(3):553–581, 2021.

[4] J Zhang, JJ Cunningham, JS Brown, and RA Gatenby. Integrating evolutionary dynamics into treatment of metastatic castrate-resistant prostate cancer. Nature communications 8, no. 1 (2017): 1816.