Bayesian Optimization with Transformed Additive Gaussian Processes

Bayesian optimization is commonly used to optimize black-box functions associated with simulations in engineering and science. Bayesian optimization contains two essential components: the acquisition function and the statistical surrogate model. In each step of Bayesian optimization, an input point is selected for a new simulation run by optimizing the acquisition function derived based on the assumptions of the surrogate statistical model. For black-box functions with higher-dimensional input, it can be a challenging problem to optimize the acquisition function in each step. To solve this challenge, we propose to use transformed additive Gaussian processes [5] as the surrogate statistical model. Therefore, we can simplify the optimization of the acquisition function by decomposing the objective function into additive one-dimensional problems. The acquisition function is then optimized for each dimension, and the new points selected from each dimension are combined to create the new input point. We evaluate the performance of the proposed method through numerical examples by comparing with classical Bayesian optimization with expected improvement.