Online Sharp-Calibrated Bayesian Optimization

TL;DR

This paper introduces OSCBO, an adaptive Bayesian optimization method that maintains sharp and well-calibrated uncertainty estimates, ensuring strong theoretical guarantees and competitive empirical performance.

Contribution

It proposes a novel online hyperparameter tuning approach for BO that balances sharpness and calibration, preserving regret bounds.

Findings

OSCBO achieves competitive simple regret on benchmarks.

It maintains robust cumulative regret behavior.

The method adapts hyperparameters online to improve uncertainty calibration.

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.