# A General Framework for Constrained Bayesian Optimization using Information-based Search

Hernández-Lobato, JM and Gelbart, MA and Adams, RP and Hoffman, MW and Ghahramani, Z (2016) A General Framework for Constrained Bayesian Optimization using Information-based Search. Journal of Machine Learning Research, 17.

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## Abstract

We present an information-theoretic framework for solving global black-box optimization problems that also have black-box constraints. Of particular interest to us is to efficiently solve problems with $\textit{decoupled}$ constraints, in which subsets of the objective and constraint functions may be evaluated independently. For example, when the objective is evaluated on a CPU and the constraints are evaluated independently on a GPU. These problems require an acquisition function that can be separated into the contributions of the individual function evaluations. We develop one such acquisition function and call it Predictive Entropy Search with Constraints (PESC). PESC is an approximation to the expected information gain criterion and it compares favorably to alternative approaches based on improvement in several synthetic and real-world problems. In addition to this, we consider problems with a mix of functions that are fast and slow to evaluate. These problems require balancing the amount of time spent in the meta-computation of PESC and in the actual evaluation of the target objective. We take a bounded rationality approach and develop a partial update for PESC which trades off accuracy against speed. We then propose a method for adaptively switching between the partial and full updates for PESC. This allows us to interpolate between versions of PESC that are efficient in terms of function evaluations and those that are efficient in terms of wall-clock time. Overall, we demonstrate that PESC is an effective algorithm that provides a promising direction towards a unified solution for constrained Bayesian optimization.

Item Type: Article Bayesian optimization constraints predictive entropy search UNSPECIFIED Div F > Computational and Biological Learning Cron Job 17 Jul 2017 19:34 31 Aug 2017 01:22