Predictive Entropy Search for Multi-objective Bayesian Optimization

TL;DR

PESMO is a Bayesian approach for multi-objective optimization that efficiently identifies Pareto sets by reducing entropy, supporting decoupled evaluations, and scaling linearly with the number of objectives.

Contribution

Introduces PESMO, a novel Bayesian method that efficiently handles multi-objective optimization with decoupled evaluations and linear scalability.

Findings

PESMO outperforms existing methods on synthetic and real-world problems.

Decoupled evaluations improve performance, especially with many objectives.

PESMO scales linearly with the number of objectives.

Abstract

We present PESMO, a Bayesian method for identifying the Pareto set of multi-objective optimization problems, when the functions are expensive to evaluate. The central idea of PESMO is to choose evaluation points so as to maximally reduce the entropy of the posterior distribution over the Pareto set. Critically, the PESMO multi-objective acquisition function can be decomposed as a sum of objective-specific acquisition functions, which enables the algorithm to be used in \emph{decoupled} scenarios in which the objectives can be evaluated separately and perhaps with different costs. This decoupling capability also makes it possible to identify difficult objectives that require more evaluations. PESMO also offers gains in efficiency, as its cost scales linearly with the number of objectives, in comparison to the exponential cost of other methods. We compare PESMO with other related methods for multi-objective Bayesian optimization on synthetic and real-world problems. The results show that PESMO produces better recommendations with a smaller number of evaluations of the objectives, and that a decoupled evaluation can lead to improvements in performance, particularly when the number of objectives is large.