Bayesian Optimization with Ensemble Learning Models and Adaptive Expected Improvement

Abstract

Optimizing a black-box function that is expensive to evaluate emerges in a gamut of machine learning and artificial intelligence applications including drug discovery, policy optimization in robotics, and hyperparameter tuning of learning models to list a few. Bayesian optimization (BO) provides a principled framework to find the global optimum of such functions using a limited number of function evaluations. BO relies on a statistical surrogate model to actively select new query points, that is typically captured by a Gaussian process (GP). Unlike most existing approaches that hinge on a single GP surrogate model with a pre-selected kernel function that may confine the expressiveness of the sought function especially under the limited evaluation budget, the present work puts forth a weighted ensemble of GPs as a surrogate model. Building on the advocated Gaussian mixture (GM) posterior, the EGP framework adapts to the most fitted surrogate model as data arrive on-the-fly, offering a richer function space. For the acquisition of next evaluation points, the EGP-based posterior is coupled with an adaptive expected improvement (EI) criterion to balance exploration and exploitation of the search space. Numerical tests on a set of benchmark synthetic functions and two robotic tasks, demonstrate the impressive benefits of the proposed approach.