Predictive Entropy Search for Bayesian Optimization with Unknown Constraints

TL;DR

This paper introduces PESC, an information-based Bayesian optimization method for problems with unknown constraints, addressing limitations of EI-based approaches and demonstrating superior performance on synthetic, benchmark, and real-world problems.

Contribution

The paper proposes PESC, a novel information-based Bayesian optimization algorithm that effectively handles unknown constraints and overcomes issues associated with expected improvement methods.

Findings

PESC outperforms EI-based methods on synthetic and benchmark problems.

PESC is effective on real-world constrained optimization tasks.

The method provides a unified approach for constrained Bayesian optimization.

Abstract

Unknown constraints arise in many types of expensive black-box optimization problems. Several methods have been proposed recently for performing Bayesian optimization with constraints, based on the expected improvement (EI) heuristic. However, EI can lead to pathologies when used with constraints. For example, in the case of decoupled constraints---i.e., when one can independently evaluate the objective or the constraints---EI can encounter a pathology that prevents exploration. Additionally, computing EI requires a current best solution, which may not exist if none of the data collected so far satisfy the constraints. By contrast, information-based approaches do not suffer from these failure modes. In this paper, we present a new information-based method called Predictive Entropy Search with Constraints (PESC). We analyze the performance of PESC and show that it compares favorably to EI-based approaches on synthetic and benchmark problems, as well as several real-world examples. We demonstrate that PESC is an effective algorithm that provides a promising direction towards a unified solution for constrained Bayesian optimization.