Tree ensemble kernels for Bayesian optimization with known constraints over mixed-feature spaces
This work addresses black-box optimization problems, such as algorithm tuning and neural architecture search, by improving efficiency in mixed-feature spaces with known constraints, representing an incremental advancement.
The paper tackles the challenges of using tree ensembles for black-box optimization by proposing a kernel interpretation to estimate model uncertainty and developing an optimization formulation for acquisition functions, which also integrates known constraints. It performs as well as state-of-the-art methods in unconstrained settings and outperforms competitors in mixed-feature spaces with constraints.
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.