用维纳核回归提升贝叶斯优化的安全性，让探索更安心。
Towards safe Bayesian optimization with Wiener kernel regression
- 基于维纳核回归构建更紧致的不确定性界
- 在温和假设下比已有界更紧，安全区域更大
- 适合对安全性要求高的黑箱优化场景
贝叶斯优化（BO）是一种基于概率代理模型的数据驱动策略，用于最小化或最大化黑箱函数。在存在安全约束的情况下，BO的性能关键依赖于代理模型不确定性的紧致概率误差界。针对高斯过程代理模型与高斯测量噪声的情形，本文提出一种基于最新提出的维纳核回归的新型误差界。我们证明，在相对温和的假设下，所提误差界优于文献中已有的边界，从而扩大了安全区域。通过数值例子展示了该误差界在安全贝叶斯优化中的有效性。
原文摘要 · Abstract (English)
Bayesian Optimization (BO) is a data-driven strategy for minimizing/maximizing black-box functions based on probabilistic surrogate models. In the presence of safety constraints, the performance of BO crucially relies on tight probabilistic error bounds related to the uncertainty surrounding the surrogate model. For the case of Gaussian Process surrogates and Gaussian measurement noise, we present a novel error bound based on the recently proposed Wiener kernel regression. We prove that under rather mild assumptions, the proposed error bound is tighter than bounds previously documented in the literature, leading to enlarged safety regions. We draw upon a numerical example to demonstrate the efficacy of the proposed error bound in safe BO.
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