Constrained Bayesian Optimization with a Cardiovascular Application

The present paper investigates constrained global optimization techniques for computationally expensive black box functions that are globally defined but subject to some a priori unknown taboo regions. This challenge typically arises in healthcare applications, where the goal is to maximize the efficacy of a drug while staying within critical safety limits imposed by an external medical regulator. Motivated by the additional challenge where the constrained global optimum lies along the constraint boundary, we comparatively assess the performance of established optimization methods coupled with different acquisition functions in terms of accuracy and efficiency on the physiological application aforementioned and several benchmark problems representative of the complexity of the physiological application. We find the best method based on an average score computed across all applications. We also propose an ensemble method combining results from individual methods, which vastly outperforms the best average method. Furthermore, our study provides a thorough qualitative analysis of the optimization results, emphasizing the challenges a user may encounter when applying Bayesian optimization on constrained optimization problems.