在线锐化校准贝叶斯优化
Online Sharp-Calibrated Bayesian Optimization
- ELLIS Institute Finland（芬兰ELLIS研究所）
- Aalto University（阿尔托大学）
- University of Manchester（曼彻斯特大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出在线锐化校准贝叶斯优化算法，通过将超参数选择转化为约束在线学习问题，平衡高斯过程的锐度和校准，保持子线性 regrets 并在合成和现实基准中表现优异。
AI中文摘要：
贝叶斯优化（BO）是一种用于优化昂贵黑盒函数的广泛使用的框架，通常基于高斯过程（GP）替代模型。其有效性依赖于在BO轨迹上既锐（信息丰富）又校准良好的不确定性量化。在实践中，GP核超参数是未知的，并且从顺序收集（非i.i.d.）数据中在线重新拟合，这可能导致校准不当或过度保守的不确定性，这超出了标准BO regrets 理论的固定核假设。我们提出在线锐化校准贝叶斯优化（OSCBO），一种将超参数选择转化为约束在线学习问题的BO算法，从而自适应地平衡GP的锐度和校准。我们还展示OSCBO通过利用底层在线学习算法的理论保证来保持子线性regret界限。在经验上，OSCBO在合成和现实基准中表现竞争，其最终简单regret排名在最强方法中，同时保持鲁棒的累积regret行为。
英文摘要：
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.
