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

원문 초록

Scientific design often requires balancing competing objectives that are expensive to evaluate through experiments or simulations. Multi-objective Bayesian optimization (MOBO) addresses this challenge by using probabilistic models to guide the selection of promising designs. In many applications, tunable inputs map to observable intermediate responses, which are then combined through known functions to compute the final objectives. Prior work on Bayesian optimization of composite functions shows that learning from these intermediate responses, which we call Composite modeling, can substantially improve sampling efficiency in single-objective optimization, compared to methods that condition only on black-box observations of the objective function. The benefits of Composite modeling in MOBO, however, remain understudied. In this work, we study the benefits of Composite modeling in MOBO and investigate the factors driving variation in its gains. We first establish single-objective conditions under which intermediate observations provide no additional predictive information beyond objective values, where composite and black box methods use the same warped Gaussian process prior. Controlled numerical experiments with versions of four MOBO methods across eight synthetic and application-inspired scientific-design benchmarks examine how these conditions relate to optimization gains in the multi-objective setting, where the black box approach models the objective functions with a standard multi-output Gaussian process. Both investigations support the claim that composite modeling tends to help more when the function mapping intermediate responses to final objectives is non-bijective and non-affine.