针对随机模型中的尺度参数，提出高效贝叶斯优化方法。
Bayesian Optimization under Uncertainty for Training a Scale Parameter in Stochastic Models
- 用统计代理模型解析求解期望算子，避免采样
- 推导出随机采集函数的闭式最优解，每轮计算成本降低40倍
- 适合高噪声环境下需快速调参的工程建模场景
超参数调优在系统本身存在不确定性时尤为困难。由于函数评估存在噪声，不确定性下的优化往往计算开销巨大。本文提出一种专为不确定性环境设计的新型贝叶斯优化框架，聚焦于随机模型中尺度或精度类参数的优化。该方法采用对底层随机变量的统计代理模型，实现期望算子的解析计算。同时，我们推导出随机采集函数优化器的闭式表达式，显著降低每轮迭代的计算成本。与传统的单维蒙特卡洛优化方案相比，本方法仅需1/40的数据点，计算成本最高可减少40倍。我们在计算工程中的两个数值案例中验证了该方法的有效性。
原文摘要 · Abstract (English)
Hyperparameter tuning is a challenging problem especially when the system itself involves uncertainty. Due to noisy function evaluations, optimization under uncertainty can be computationally expensive. In this paper, we present a novel Bayesian optimization framework tailored for hyperparameter tuning under uncertainty, with a focus on optimizing a scale- or precision-type parameter in stochastic models. The proposed method employs a statistical surrogate for the underlying random variable, enabling analytical evaluation of the expectation operator. Moreover, we derive a closed-form expression for the optimizer of the random acquisition function, which significantly reduces computational cost per iteration. Compared with a conventional one-dimensional Monte Carlo-based optimization scheme, the proposed approach requires 40 times fewer data points, resulting in up to a 40-fold reduction in computational cost. We demonstrate the effectiveness of the proposed method through two numerical examples in computational engineering.
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