Bayesian optimization under mixed constraints with a slack-variable augmented Lagrangian

Abstract

An augmented Lagrangian (AL) can convert a constrained optimization problem into a sequence of simpler (e.g., unconstrained) problems, which are then usually solved with local solvers. Recently, surrogate-based Bayesian optimization (BO) sub-solvers have been successfully deployed in the AL framework for a more global search in the presence of inequality constraints; however, a drawback was that expected improvement (EI) evaluations relied on Monte Carlo. Here we introduce an alternative slack variable AL, and show that in this formulation the EI may be evaluated with library routines. The slack variables furthermore facilitate equality as well as inequality constraints, and mixtures thereof. We show how our new slack "ALBO" compares favorably to the original. Its superiority over conventional alternatives is reinforced on several mixed constraint examples.

arXiv comment24 pages, 5 figures

References in corpus (4)

• Practical Bayesian Optimization of Machine Learning Algorithms
• A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning
• Bayesian Optimization with Unknown Constraints
• Predictive Entropy Search for Bayesian Optimization with Unknown Constraints

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