提出随机化方法自动选择参数，提升不确定输入下鲁棒性优化效果。
Bayesian Optimization of Robustness Measures under Input Uncertainty: A Randomized Gaussian Process Upper Confidence Bound Approach
- 从卡方分布采样超参数β，无需手动设定
- 理论证明预期损失有紧致上界
- 适合需要自动调参的黑箱优化场景
基于高斯过程上置信界（GP-UCB）的贝叶斯优化为黑箱函数优化提供了理论保障。然而实际中，黑箱函数常面临输入不确定性。为此，可通过优化称为鲁棒性度量的评估准则来应对。但现有的基于GP-UCB的鲁棒性优化方法需设置超参数β，且必须足够大以保证理论有效性。本文提出随机化鲁棒性度量GP-UCB（RRGP-UCB），从基于卡方分布的概率分布中采样β，无需显式指定β。该分布下β的期望值并不过大。进一步证明，RRGP-UCB能提供最优解与估计解之间预期遗憾的紧致上界。数值实验验证了该方法的有效性。
原文摘要 · Abstract (English)
Bayesian optimization based on the Gaussian process upper confidence bound (GP-UCB) offers a theoretical guarantee for optimizing black-box functions. In practice, however, black-box functions often involve input uncertainty. To handle such cases, GP-UCB can be extended to optimize evaluation criteria known as robustness measures. However, GP-UCB-based methods for robustness measures require a trade-off parameter, $β$, which, as in the original GP-UCB, must be set sufficiently large to ensure theoretical validity. In this study, we propose randomized robustness measure GP-UCB (RRGP-UCB), a novel method that samples $β$ from a chi-squared-based probability distribution. This approach eliminates the need to explicitly specify $β$. Notably, the expected value of $β$ under this distribution is not excessively large. Furthermore, we show that RRGP-UCB provides tight bounds on the expected regret between the optimal and estimated solutions. Numerical experiments demonstrate the effectiveness of the proposed method.
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