Gaussian Process Sampling and Optimization with Approximate Upper and Lower Bounds

TL;DR

This paper introduces Gaussian process models that incorporate approximate bounds on functions to improve posterior sampling and Bayesian optimization, providing a new way to exploit known bounds for better decision-making.

Contribution

It presents the first method to integrate approximate bounds into Gaussian process models for enhanced sampling and optimization, including a bounded entropy search strategy.

Findings

Bounded entropy search effectively selects informative points under constraints.

The proposed methods are straightforward to implement as extensions to existing GP techniques.

The approach improves the explainability and efficiency of Bayesian optimization with bounds.

Abstract

Many functions have approximately-known upper and/or lower bounds, potentially aiding the modeling of such functions. In this paper, we introduce Gaussian process models for functions where such bounds are (approximately) known. More specifically, we propose the first use of such bounds to improve Gaussian process (GP) posterior sampling and Bayesian optimization (BO). That is, we transform a GP model satisfying the given bounds, and then sample and weight functions from its posterior. To further exploit these bounds in BO settings, we present bounded entropy search (BES) to select the point gaining the most information about the underlying function, estimated by the GP samples, while satisfying the output constraints. We characterize the sample variance bounds and show that the decision made by BES is explainable. Our proposed approach is conceptually straightforward and can be used as a plug in extension to existing methods for GP posterior sampling and Bayesian optimization.