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.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.10572 [cs.LG] |
| (or arXiv:2605.10572v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.10572 arXiv-issued DOI via DataCite (pending registration) |
From: Marshal Arijona Sinaga [view email]
[v1]
Mon, 11 May 2026 13:41:42 UTC (5,515 KB)
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