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

TL;DR

This paper introduces a slack-variable augmented Lagrangian method for Bayesian optimization that allows efficient expected improvement evaluation with standard routines, improving handling of mixed equality and inequality constraints.

Contribution

The paper proposes a novel slack-variable augmented Lagrangian approach for Bayesian optimization, enabling EI evaluation with library routines and better handling of mixed constraints.

Findings

Slack-variable AL allows EI evaluation with standard routines.

The method effectively handles mixed equality and inequality constraints.

Experimental results show superior performance over traditional methods.

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.