Predictive Entropy Search for Multi-objective Bayesian Optimization with Constraints

TL;DR

This paper introduces PESMOC, an information-based Bayesian optimization method for efficiently solving multi-objective problems with expensive, noisy constraints, outperforming random search in synthetic experiments.

Contribution

PESMOC is a novel method that extends predictive entropy search to handle multiple objectives and constraints in Bayesian optimization.

Findings

PESMOC reduces the number of evaluations needed for optimal solutions.

PESMOC outperforms random search in synthetic experiments.

The method effectively handles noisy, expensive constraints.

Abstract

This work presents PESMOC, Predictive Entropy Search for Multi-objective Bayesian Optimization with Constraints, an information-based strategy for the simultaneous optimization of multiple expensive-to-evaluate black-box functions under the presence of several constraints. PESMOC can hence be used to solve a wide range of optimization problems. Iteratively, PESMOC chooses an input location on which to evaluate the objective functions and the constraints so as to maximally reduce the entropy of the Pareto set of the corresponding optimization problem. The constraints considered in PESMOC are assumed to have similar properties to those of the objective functions in typical Bayesian optimization problems. That is, they do not have a known expression (which prevents gradient computation), their evaluation is considered to be very expensive, and the resulting observations may be corrupted by noise. These constraints arise in a plethora of expensive black-box optimization problems. We carry out synthetic experiments to illustrate the effectiveness of PESMOC, where we sample both the objectives and the constraints from a Gaussian process prior. The results obtained show that PESMOC is able to provide better recommendations with a smaller number of evaluations than a strategy based on random search.