arXiv:2605.20145stat.MLcs.LG2026-05

针对贝叶斯优化中低尾预测不准问题,提出后处理校准方法提升搜索效率。

Goal-Oriented Lower-Tail Calibration of Gaussian Processes for Bayesian Optimization

  • 基于空间校准思想,对低阈值以下的预测分布进行定向校准
  • 实验显示在标准测试集上校准效果和优化性能均优于传统GP模型
  • 特别适合追求高精度搜索的黑箱优化场景

贝叶斯优化通过高斯过程(GP)的预测分布选择昂贵黑箱目标函数的评估点。核函数选择与超参数估计可能导致预测分布失准,影响探索与利用的平衡。对于最小化任务,期望改进(EI)等采样准则依赖于当前最优值以下的预测分布,因此低尾失准会直接影响采样决策。本文研究在无噪声设定下,使用最大似然法选择超参数的标准GP模型在低阈值 $t$ 以下的定向校准问题。提出一个基于两种空间校准概念的可靠性框架:设计空间上的发生校准,以及子水平集 $\\

原文摘要 · Abstract (English)

Bayesian optimization (BO) selects evaluation points for expensive black-box objectives using Gaussian process (GP) predictive distributions. Kernel choice and hyperparameter selection can lead to miscalibrated predictive distributions and an inappropriate exploration-exploitation trade-off. For minimization, sampling criteria such as expected improvement (EI) depend on the predictive distribution below the current best value, so lower-tail miscalibration directly affects the sampling decision. This article studies goal-oriented calibration of GP predictive distributions below a low threshold $t$ in the noiseless setting, for standard GP models with hyperparameters selected by maximum likelihood. A framework for predictive reliability below $t$ is introduced, based on two notions of spatial calibration: occurrence calibration over the design space and thresholded $μ$-calibration on sublevel sets of the form $\{x\in\mathbb{X}, f(x)\le t\}$. Building on this framework, we propose tcGP, a post-hoc method that calibrates GP predictive distributions below~$t$, and we show that the resulting EI-based global optimization algorithm remains dense in the design space. Experiments on standard benchmarks show improved lower-tail calibration and BO performance relative to standard GP models and globally calibrated GP models.

贝叶斯优化高斯过程校准黑箱优化

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