Scalable Bayesian Optimization Using Vecchia Approximations of Gaussian Processes

TL;DR

This paper introduces a scalable Bayesian optimization method using Vecchia approximations of Gaussian processes, enabling efficient high-dimensional optimization with improved performance over existing methods.

Contribution

It adapts the Vecchia approximation for Gaussian processes to high-dimensional Bayesian optimization, including novel training and parallelization techniques.

Findings

Outperforms state-of-the-art methods on test functions

Effective in high-dimensional reinforcement learning tasks

Enables scalable Bayesian optimization with improved accuracy

Abstract

Bayesian optimization is a technique for optimizing black-box target functions. At the core of Bayesian optimization is a surrogate model that predicts the output of the target function at previously unseen inputs to facilitate the selection of promising input values. Gaussian processes (GPs) are commonly used as surrogate models but are known to scale poorly with the number of observations. We adapt the Vecchia approximation, a popular GP approximation from spatial statistics, to enable scalable high-dimensional Bayesian optimization. We develop several improvements and extensions, including training warped GPs using mini-batch gradient descent, approximate neighbor search, and selecting multiple input values in parallel. We focus on the use of our warped Vecchia GP in trust-region Bayesian optimization via Thompson sampling. On several test functions and on two reinforcement-learning problems, our methods compared favorably to the state of the art.