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Predictive Entropy Search for Bayesian Optimization with Unknown Constraints
"... Unknown constraints arise in many types of ex-pensive black-box optimization problems. Sev-eral methods have been proposed recently for performing Bayesian optimization with con-straints, based on the expected improvement (EI) heuristic. However, EI can lead to pathologies when used with constraints ..."
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Unknown constraints arise in many types of ex-pensive black-box optimization problems. Sev-eral methods have been proposed recently for performing Bayesian optimization with con-straints, 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 sat-isfy the constraints. By contrast, information-based approaches do not suffer from these fail-ure modes. In this paper, we present a new information-based method called Predictive En-tropy Search with Constraints (PESC). We ana-lyze 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.
