Gaussian Process

Goal-Oriented Lower-Tail Calibration of Gaussian Processes for Bayesian Optimization

This paper addresses miscalibration in Gaussian process predictive distributions used for Bayesian optimization, focusing specifically on the lower tail relevant to minimization objectives. The authors introduce a framework for 'goal-oriented' spatial calibration below a threshold t, defining occurrence calibration and thresholded μ-calibration on sublevel sets. They propose tcGP, a post-hoc calibration method, and prove the resulting EI-based optimizer remains dense in the design space. Experiments on standard benchmarks show tcGP improves both lower-tail calibration and overall BO performance compared to standard and globally calibrated GP models.