Investigating Composite Modeling in Multi-Objective Bayesian Optimization for Scientific Design

Scientific design often requires balancing expensive, competing objectives using few experiments or simulations. Multi-objective Bayesian optimization (MOBO) uses Gaussian processes (GPs) to model the final objectives and sequentially selects promising designs using an acquisition function based on these models. However, in many applications, the final objectives combine observable intermediate responses through known functions, a structure that standard MOBO ignores. Prior work in single-objective optimization shows that modeling the intermediate responses with GPs and propagating their posterior distributions through the known functions to obtain posterior distributions over the final objectives can improve optimization performance. However, the value of this Composite modeling approach in MOBO remains unclear. Across eight low- and high-dimensional synthetic and application-inspired scientific and engineering design problems, we compare Direct versions that ignore this structure with Composite versions that exploit it for four MOBO methods. Composite modeling improves performance in most comparisons, but its gains vary substantially across problems and methods. By examining problems with large and small gains, we use our initial observations to motivate hypotheses about when Composite modeling is beneficial and propose a more systematic and rigorous approach for future investigation. Our work serves as an initial step toward characterizing when scientific design problems benefit from Composite modeling.