We introduce variational sequential Optimal Experimental Design (vsOED), a new method for optimally designing a finite sequence of experiments under a Bayesian framework and with information-gain utilities. Specifically, we adopt a lower bound estimator for the expected utility through variational approximation to the Bayesian posteriors. The optimal design policy is solved numerically by simultaneously maximizing the variational lower bound and performing policy gradient updates. We demonstrate this general methodology for a range of OED problems targeting parameter inference, model discrimination, and goal-oriented prediction. These cases encompass explicit and implicit likelihoods, nuisance parameters, and physics-based partial differential equation models. Our vsOED results indicate substantially improved sample efficiency and reduced number of forward model simulations compared to previous sequential design algorithms.

翻译：我们提出了变分序列最优实验设计（vsOED），一种在贝叶斯框架下以信息增益效用函数最优地设计有限实验序列的新方法。具体而言，我们通过变分近似贝叶斯后验分布，构建了期望效用的下界估计量。通过同时最大化变分下界和执行策略梯度更新，数值求解最优设计策略。我们针对参数推断、模型辨识与目标导向预测等典型最优实验设计问题，验证了该通用方法的有效性。这些案例涵盖显式与隐式似然函数、冗余参数以及基于物理的偏微分方程模型。与现有序列设计算法相比，vsOED显著提升了样本效率，并减少了前向模型仿真次数。