We propose a variance-penalized formulation of Bayesian optimal experimental design for nonlinear models that augments the classical expected utility criterion with a penalty on utility variability, yielding a mean--variance objective that promotes robust experimental performance. To evaluate this objective, we develop Monte Carlo estimators for the expected utility, its second moment, and the resulting utility variance using prior sampling, thereby avoiding explicit posterior sampling. We then derive leading-order bias and variance expressions using conditional delta-method arguments. The objective is optimized using Bayesian optimization with common random samples to reduce noise. Numerical examples, including a linear-Gaussian benchmark, a nonlinear test problem, and contaminant source inversion in diffusion fields, demonstrate that the proposed approach identifies designs with substantially reduced variability while maintaining competitive expected utility.

翻译：我们提出了一种针对非线性模型的贝叶斯最优实验设计的方差惩罚形式，该方法在经典期望效用准则中引入效用变异性的惩罚项，构建了一个促进鲁棒实验性能的均值-方差目标函数。为评估该目标函数，我们基于先验采样发展了期望效用、二阶矩及相应效用方差的蒙特卡洛估计量，从而避免了显式的后验采样。随后通过条件delta-method论证推导了主导阶偏差和方差表达式。该目标函数采用共享随机样本的贝叶斯优化方法进行优化以降低噪声。数值实验（包括线性高斯基准问题、非线性测试问题以及扩散场中的污染源反演）表明，所提方法在保持具有竞争力期望效用的同时，能够识别出显著降低变异性的设计方案。