A survey on high-dimensional Gaussian process modeling with application to Bayesian optimization

TL;DR

This survey reviews high-dimensional Gaussian process modeling techniques in Bayesian optimization, discussing various structural assumptions and their practical advantages and limitations for optimizing complex, high-dimensional functions.

Contribution

It provides a comprehensive overview of structural model assumptions in high-dimensional Gaussian process regression for Bayesian optimization, highlighting their practical benefits and challenges.

Findings

Structural assumptions improve high-dimensional BO efficiency.

Trade-offs exist between model complexity and optimization performance.

Different approaches have varying suitability depending on problem structure.

Abstract

Bayesian Optimization, the application of Bayesian function approximation to finding optima of expensive functions, has exploded in popularity in recent years. In particular, much attention has been paid to improving its efficiency on problems with many parameters to optimize. This attention has trickled down to the workhorse of high dimensional BO, high dimensional Gaussian process regression, which is also of independent interest. The great flexibility that the Gaussian process prior implies is a boon when modeling complicated, low dimensional surfaces but simply says too little when dimension grows too large. A variety of structural model assumptions have been tested to tame high dimensions, from variable selection and additive decomposition to low dimensional embeddings and beyond. Most of these approaches in turn require modifications of the acquisition function optimization strategy as well. Here we review the defining structural model assumptions and discuss the benefits and drawbacks of these approaches in practice.