Targeting Solutions in Bayesian Multi-Objective Optimization: Sequential and Batch Versions
This work addresses the challenge of efficiently finding specific trade-off solutions in multi-objective optimization for users dealing with costly evaluations, though it is incremental as it modifies an existing algorithm.
The authors tackled the problem of focusing Bayesian multi-objective optimization on user-preferred regions of the Pareto set for expensive-to-evaluate functions, resulting in particularly efficient convergence to the desired part of the Pareto set.
Multi-objective optimization aims at finding trade-off solutions to conflicting objectives. These constitute the Pareto optimal set. In the context of expensive-to-evaluate functions, it is impossible and often non-informative to look for the entire set. As an end-user would typically prefer a certain part of the objective space, we modify the Bayesian multi-objective optimization algorithm which uses Gaussian Processes to maximize the Expected Hypervolume Improvement, to focus the search in the preferred region. The cumulated effects of the Gaussian Processes and the targeting strategy lead to a particularly efficient convergence to the desired part of the Pareto set. To take advantage of parallel computing, a multi-point extension of the targeting criterion is proposed and analyzed.