Tree ensemble kernels for Bayesian optimization with known constraints over mixed-feature spaces

TL;DR

This paper introduces a kernel-based Gaussian Process approach using tree ensembles for constrained black-box optimization over mixed feature spaces, improving uncertainty quantification and optimization efficiency.

Contribution

It proposes a novel kernel interpretation of tree ensembles as Gaussian Processes, enabling effective uncertainty estimation and constraint handling in Bayesian optimization.

Findings

Performs comparably to state-of-the-art in unconstrained settings.

Outperforms existing methods in constrained mixed-variable problems.

Effectively incorporates domain knowledge and symmetries.

Abstract

Tree ensembles can be well-suited for black-box optimization tasks such as algorithm tuning and neural architecture search, as they achieve good predictive performance with little or no manual tuning, naturally handle discrete feature spaces, and are relatively insensitive to outliers in the training data. Two well-known challenges in using tree ensembles for black-box optimization are (i) effectively quantifying model uncertainty for exploration and (ii) optimizing over the piece-wise constant acquisition function. To address both points simultaneously, we propose using the kernel interpretation of tree ensembles as a Gaussian Process prior to obtain model variance estimates, and we develop a compatible optimization formulation for the acquisition function. The latter further allows us to seamlessly integrate known constraints to improve sampling efficiency by considering domain-knowledge in engineering settings and modeling search space symmetries, e.g., hierarchical relationships in neural architecture search. Our framework performs as well as state-of-the-art methods for unconstrained black-box optimization over continuous/discrete features and outperforms competing methods for problems combining mixed-variable feature spaces and known input constraints.