Constrained Multi-objective Bayesian Optimization through Optimistic Constraints Estimation

Multi-objective Bayesian optimization (MBO) plays a critical role in various scientific fields, particularly where experimental efficiency and precision are paramount. In drug discovery, for example, researchers must navigate a vast experimental space, balancing multiple objectives like maximizing therapeutic efficacy while minimizing toxicity and adverse effects (Fromer and Coley, 2023). The challenge lies not only in identifying promising drug candidates but also in meeting stringent regulatory and safety requirements, which impose additional constraints on the optimization process (Mellinghoff and Cloughesy, 2022). A failure to meet these regulatory and safety constraints can lead to significant delays in clinical trials or even abandonment of potential drug candidates. Similarly, in hyper-parameter optimization for machine learning models, there is a need to balance model accuracy, recall, and robustness to distribution shift (Gardner et al., 2019). Here, efficient exploration of hyper-parameter space must also respect practical constraints, such as avoiding configurations that lead to excessively high training times or resource overuse (Karl et al., 2023). Those practical considerations motivate the constrained multi-objective Bayesian optimization (Fernández-Sánchez et al., 2023; Hernández-Lobato et al., 2016) beyond MBO. Research in Bayesian Optimization (BO) has mainly focused on unconstrained problems, with Constrained Bayesian Optimization (CBO) evolving from early work by Schonlau et al. (1998). Subsequent efforts introduced posterior sampling (Eriksson and Poloczek, 2021) and informationbased methods (Hernández-Lobato et al., 2014; Wang and Jegelka, 2017) to improve scalability and feasibility analysis (Hernández-Lobato et al., 2015; Perrone et al., 2019; Takeno et al., 2022).