# Online Sharp-Calibrated Bayesian Optimization

arXiv: https://arxiv.org/abs/2605.10572 · HTML: https://mlsanity.com/paper/2605.10572/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 36 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 24 of 24)

- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Online Learning: A Modern Introduction Using Convex Optimization](https://mlsanity.com/paper/1912.13213/) (2019)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences](https://mlsanity.com/paper/1807.02582/) (2018)
- [TabICLv2: A better, faster, scalable, and open tabular foundation model](https://mlsanity.com/paper/2602.11139/) (2026)
- [Accelerating Bayesian Optimization for Biological Sequence Design with Denoising Autoencoders](https://mlsanity.com/paper/2203.12742/) (2022)
- [Vanilla Bayesian Optimization Performs Great in High Dimensions](https://mlsanity.com/paper/2402.02229/) (2024)
- [PFNs4BO: In-Context Learning for Bayesian Optimization](https://mlsanity.com/paper/2305.17535/) (2023)
- [Online conformal prediction with decaying step sizes](https://mlsanity.com/paper/2402.01139/) (2024)
- [No-Regret Bayesian Optimization with Unknown Hyperparameters](https://mlsanity.com/paper/1901.03357/) (2019)
- [A Study of Bayesian Neural Network Surrogates for Bayesian Optimization](https://mlsanity.com/paper/2305.20028/) (2023)
- [A Unifying Framework for Online Optimization with Long-Term Constraints](https://mlsanity.com/paper/2209.07454/) (2022)
- [Online Non-Convex Learning: Following the Perturbed Leader is Optimal](https://mlsanity.com/paper/1903.08110/) (2019)
- [Regret bounds for meta Bayesian optimization with an unknown Gaussian process prior](https://mlsanity.com/paper/1811.09558/) (2018)
- [Bayesian Optimization with Conformal Prediction Sets](https://mlsanity.com/paper/2210.12496/) (2022)
- [Online Calibrated and Conformal Prediction Improves Bayesian Optimization](https://mlsanity.com/paper/2112.04620/) (2021)
- [Beyond Primal-Dual Methods in Bandits with Stochastic and Adversarial Constraints](https://mlsanity.com/paper/2405.16118/) (2024)
- [Bayesian Optimisation with Unknown Hyperparameters: Regret Bounds Logarithmically Closer to Optimal](https://mlsanity.com/paper/2410.10384/) (2024)
- [Sharp Calibrated Gaussian Processes](https://mlsanity.com/paper/2302.11961/) (2023)
- [Adaptation to Misspecified Kernel Regularity in Kernelised Bandits](https://mlsanity.com/paper/2304.13830/) (2023)
- [Calibrated Regression Against An Adversary Without Regret](https://mlsanity.com/paper/2302.12196/) (2023)

## Abstract (arXiv)

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.