Bayesian multi-objective optimization for stochastic simulators: an extension of the Pareto Active Learning method

Examples can be found in all areas of engineering and science, for instance plant breeding (Hunter & McClosky, 2016), aircraft maintenance (Mattila & Virtanen, 2014) or electric network planning (Dutrieux et al., 2015b). In this work, we choose to focus on Bayesian optimization algorithms, which use probabilistic models to make predictions about the functions to be optimized. One of the classical algorithms for Bayesian deterministic multi-objective optimization is the ParEGO algorithm (Knowles, 2006). It relies on a scalarization approach to extend the very popular single-objective Efficient Global Optimization (EGO) algorithm (Jones et al., 1998), based on the Expected Improvement (EI) criterion. Another scalarization approach, called multi-attribute Knowledge Gradient (Astudillo & Frazier, 2017), uses the Knowledge Gradient (KG) criterion instead of the EI criterion.