We study stability properties of the expected utility function in Bayesian optimal experimental design. We provide a framework for this problem in a non-parametric setting and prove a convergence rate of the expected utility with respect to a likelihood perturbation. This rate is uniform over the design space and its sharpness in the general setting is demonstrated by proving a lower bound in a special case. To make the problem more concrete we proceed by considering non-linear Bayesian inverse problems with Gaussian likelihood and prove that the assumptions set out for the general case are satisfied and regain the stability of the expected utility with respect to perturbations to the observation map. Theoretical convergence rates are demonstrated numerically in three different examples.

翻译：我们研究了贝叶斯最优实验设计中期望效用函数的稳定性性质。在非参数设定下，我们为该问题构建了一个理论框架，并证明了期望效用函数关于似然扰动的收敛速率。该速率在设计空间上具有一致性，且通过特例中下界的证明，验证了其在一般设定下的尖锐性。为进一步具体化问题，我们考虑了具有高斯似然的非线性贝叶斯反问题，证明了所提出的适用于一般情形的假设条件得到满足，并恢复了期望效用函数关于观测映射扰动的稳定性。最后，通过三个不同算例对理论收敛速率进行了数值验证。