Improved Max-value Entropy Search for Multi-objective Bayesian Optimization with Constraints

Daniel Fernández-Sánchez, Eduardo C. Garrido-Merchán, Daniel Hernández-Lobato

Abstract: We present Improved Max-value Entropy search for Multi-Objective Bayesian optimization with Constraints (MESMOC+) for the constrained optimization of expensive-to-evaluate black-boxes. It is based on minimizing the entropy of the solution of the problem in function space (i.e., the Pareto front) to guide the search for the optimum. Its cost is linear in the number of black-boxes, and due to its expression, it can be used in a decoupled evaluation setting in which we chose where and also what black-box (objective or constraint) to evaluate. Our synthetic experiments show that MESMOC+ has similar performance to other state-of-the-art acquisition functions, but it is faster to execute, simpler to implement and it is more robust with respect to the number of samples of the Pareto front.

Keywords: Bayesian Optimization, Constrained Multi-Objective Scenario, Information theory

One-sentence Summary: We present MESMOC+, an improved version of Max-value Entropy search for Multi-Objective Bayesian optimization with Constraints (MESMOC) for the constrained optimization of expensive-to-evaluate black-boxes.

Reproducibility Checklist: Yes

Broader Impact Statement: Yes

Paper Availability And License: Yes

Code Of Conduct: Yes

Reviewers: Daniel Fernández-Sánchez, [e-mail]

Code And Dataset Supplement: https://anonymous.4open.science/r/AutoML22-F6E4/