Uncertainty Quantification for Bayesian Optimization
This work addresses the lack of uncertainty quantification in Bayesian optimization, which is important for practitioners needing reliable optimization outputs, though it appears incremental as it builds on existing sequential sampling policies.
The authors tackled the problem of uncertainty quantification in Bayesian optimization by proposing a method to construct confidence regions for the maximum point or value of the objective function, with results including efficient computation and guaranteed confidence levels based on new uniform error bounds.
Bayesian optimization is a class of global optimization techniques. In Bayesian optimization, the underlying objective function is modeled as a realization of a Gaussian process. Although the Gaussian process assumption implies a random distribution of the Bayesian optimization outputs, quantification of this uncertainty is rarely studied in the literature. In this work, we propose a novel approach to assess the output uncertainty of Bayesian optimization algorithms, which proceeds by constructing confidence regions of the maximum point (or value) of the objective function. These regions can be computed efficiently, and their confidence levels are guaranteed by the uniform error bounds for sequential Gaussian process regression newly developed in the present work. Our theory provides a unified uncertainty quantification framework for all existing sequential sampling policies and stopping criteria.