在线自适应调节高斯过程精度与置信度，提升贝叶斯优化稳定性。
Online Sharp-Calibrated Bayesian Optimization
- 将超参数选择转化为约束在线学习问题，动态平衡置信度与精度
- 在合成与真实场景中均实现最低最终简单损失，累积损失稳定
- 适合需要可靠不确定估计的工业级黑箱优化任务
贝叶斯优化（BO）广泛用于优化昂贵的黑箱函数，通常基于高斯过程（GP）代理模型。其有效性依赖于沿优化轨迹具有既精确又校准的不确定性量化。实践中，GP核超参数未知，需从顺序采集的非独立同分布数据中在线重拟合，这可能导致不确定性校准不足或过于保守，违背标准BO后悔理论中的固定核假设。本文提出在线锐化校准贝叶斯优化（OSCBO），通过将超参数选择建模为约束在线学习问题，自适应平衡GP的锐度与校准性。我们证明了OSCBO能保持次线性后悔界，得益于底层在线学习算法的理论保证。实验表明，OSCBO在合成与真实世界基准上表现优异，在最终简单后悔值上排名前列，同时具备稳健的累积后悔行为。
原文摘要 · Abstract (English)
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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