Profile Bayesian Optimization for Expensive Computer Experiments

We propose a novel Bayesian optimization (BO) procedure aimed at identifying the ``profile optima'' of a deterministic black-box computer simulation that has a single control parameter and multiple nuisance parameters. The profile optima capture the optimal response values as a function of the control parameter. Our objective is to identify them across the entire plausible range of the control parameter. Classic BO, which targets a single optimum over all parameters, does not explore the entire control parameter range. Instead, we develop a novel two-stage acquisition scheme to balance exploration across the control parameter and exploitation of the profile optima, leveraging deep and shallow Gaussian process surrogates to facilitate uncertainty quantification. We are motivated by a computer simulation of a diffuser in a rotating detonation combustion engine, which returns the energy lost through diffusion as a function of various design parameters. We aim to identify the lowest possible energy loss as a function of the diffuser's length; understanding this relationship will enable well-informed design choices. Our ``profile Bayesian optimization'' procedure outperforms traditional BO and profile optimization methods on a variety of benchmarks and proves effective in our motivating application.