Predictive Entropy Search for Multi-objective Bayesian Optimization with Constraints

Abstract

Este trabajo presenta PESMOC, Predictive Entropy Search for Multi-objective Bayesian Optimization with Constraints, una estrategia basada en la información para la optimización simultánea de múltiples funciones de caja negra costosas de evaluar bajo la presencia de varias restricciones. Por lo tanto, PESMOC se puede utilizar para resolver una amplia gama de problemas de optimización. Iterativamente, PESMOC elige una ubicación de entrada en la que evaluar las funciones objetivas y las restricciones para reducir al máximo la entropía del conjunto de Pareto del problema de optimización correspondiente. Se aportan multiples experimentos para demostrar que el método es el estado del arte para resolver estos escenarios.

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.