Online Sharp-Calibrated Bayesian Optimization

2026-05-11

AI Summary

This work addresses the challenge in Bayesian optimization where online tuning of Gaussian process kernel hyperparameters often leads to either poorly calibrated or overly conservative uncertainty estimates. To this end, it introduces a novel approach that formulates hyperparameter selection as a constrained online learning problem, dynamically balancing sharpness and calibration of uncertainty estimates along the optimization trajectory. The proposed method achieves adaptive control over uncertainty quality while preserving a sublinear regret bound. Empirical evaluations across multiple synthetic and real-world benchmarks demonstrate its superior performance: it consistently attains top-ranked final simple regret and maintains robust cumulative regret behavior throughout the optimization process.

Abstract

Bayesian optimization (BO) is a widely used framework for optimizing expensive black-box functions, commonly based on Gaussian process (GP) surrogate models. Its effectiveness relies on uncertainty quantification that is both sharp (informative) and well-calibrated along the BO trajectory. In practice, GP kernel hyperparameters are unknown and are refit online from sequentially collected (non-i.i.d.) data, which can yield miscalibrated or overly conservative uncertainty and lies outside the fixed-kernel assumptions of standard BO regret theory. We propose Online Sharp-Calibrated Bayesian Optimization (OSCBO), a BO algorithm that adaptively balances GP sharpness and calibration by casting hyperparameter selection as a constrained online-learning problem. We also show that OSCBO preserves sublinear regret bounds by leveraging the theoretical guarantees of the underlying online learning algorithm. Empirically, OSCBO performs competitively across synthetic and real-world benchmarks, ranking among the strongest methods in final simple regret while maintaining robust cumulative-regret behavior.

Problem

• Bayesian optimization
• Gaussian process
• uncertainty calibration
• hyperparameter selection
• online learning

Innovation

• Bayesian optimization
• Gaussian process
• uncertainty calibration
• online learning
• sharpness-calibration trade-off