通过温顺后验的鲁棒贝叶斯优化
Robust Bayesian Optimization via Tempered Posteriors
AI总结：
本文提出了一种通过温顺后验更新的鲁棒贝叶斯优化方法，以缓解局部规格不准确导致的过度自信问题，并在理论和实践中提升了优化稳定性。
摘要：
贝叶斯优化（BO）通过迭代拟合高斯过程（GP）代理模型来适应累积评估，并通过期望改进（EI）等获取函数选择新的查询。在实践中，BO经常将评估集中在当前最优解附近，导致代理模型变得过于自信，并在引导后续决策的区域下估预测不确定性。我们开发了一种基于GP的鲁棒BO方法，通过温顺后验更新，通过将似然值乘以一个功率α∈(0,1]来减轻局部规格不准确下的过度自信。我们建立了在一组广义改进规则下的累积遗憾界限，包括EI，并证明温顺BO在标准后验（α=1）的情况下提供了更严格的最坏情况遗憾保证，最有利的保证发生在经典EI选择附近。受我们理论发现的启发，我们提出了一种预quential程序用于在线选择α：当实际预测误差超过模型暗示的不确定性时，它会降低α，并在校准改善时将α返回到1。实证结果表明，温顺提供了一种实用且理论支持的工具，用于在局部采样下稳定BO代理。
英文摘要：
Bayesian optimization (BO) iteratively fits a Gaussian process (GP) surrogate to accumulated evaluations and selects new queries via an acquisition function. Under local misspecification, this feedback loop can produce overconfidence precisely in the region guiding subsequent decisions. We develop a tempered GP-based BO framework that raises the likelihood to a power $α\in(0,1]$. For a generalized family of improvement acquisitions indexed by $g$, including probability of improvement (PI, $g=0$) and expected improvement (EI, $g=1$), we derive finite-time cumulative regret bounds with adaptively learned kernel hyperparameters. The analysis shows that tempering reduces the noise-driven confidence and information-gain contributions to regret, while a deterministic RKHS term prevents arbitrarily aggressive tempering from being uniformly beneficial. It also clarifies the role of the acquisition function: positive-order $g$-EI rules preserve the usual information-gain regret behavior, whereas zero-jitter PI is more exploitative and admits a weaker worst-case guarantee. Motivated by our theoretic findings, we propose a prequential procedure for selecting $α$ online: it decreases $α$ when realized prediction errors exceed model-implied uncertainty and returns $α$ toward one as calibration improves. Empirical results demonstrate that tempering provides a practical yet theoretically grounded tool for stabilizing BO surrogates under localized sampling.
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