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arXiv · 2605.10572

Online Sharp-Calibrated Bayesian Optimization

Marshal Arijona Sinaga·Julien Martinelli·Teemu Turpeinen·Samuel Kaski
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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.

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Marshal Arijona Sinaga, Julien Martinelli, Teemu Turpeinen, Samuel Kaski. 2026-05-11. Online Sharp-Calibrated Bayesian Optimization. https://arxiv.org/abs/2605.10572

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