Gaussian Process Sampling and Optimization with Approximate Upper and Lower Bounds
This work addresses a domain-specific problem in Bayesian optimization for functions with bounds, offering an incremental improvement as a plug-in extension to existing methods.
The paper tackles the problem of modeling functions with known approximate bounds by introducing Gaussian process models that incorporate these bounds to improve posterior sampling and Bayesian optimization, resulting in bounded entropy search (BES) for explainable decision-making with characterized sample variance bounds.
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.