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Optimistic Bayesian Optimization with Unknown Constraints

Quoc Phong Nguyen · Wan Theng Ruth Chew · Le Song · Bryan Kian Hsiang Low · Patrick Jaillet

Halle B #165
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Tue 7 May 1:45 a.m. PDT — 3:45 a.m. PDT


Though some research efforts have been dedicated to constrained Bayesian optimization (BO), there remains a notable absence of a principled approach with a theoretical performance guarantee in the decoupled setting. Such a setting involves independent evaluations of the objective function and constraints at different inputs, and is hence a relaxation of the commonly-studied coupled setting where functions must be evaluated together. As a result, the decoupled setting requires an adaptive selection between evaluating either the objective function or a constraint, in addition to selecting an input (in the coupled setting). This paper presents a novel constrained BO algorithm with a provable performance guarantee that can address the above relaxed setting. Specifically, it considers the fundamental trade-off between exploration and exploitation in constrained BO, and, interestingly, affords a noteworthy connection to active learning. The performance of our proposed algorithms is also empirically evaluated using several synthetic and real-world optimization problems.

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