Bayesian experimental design (BED) provides a principled framework for optimizing data collection by choosing experiments that are maximally informative about unknown parameters. However, existing methods cannot deal with the joint challenge of (a) partially observable dynamical systems, where only noisy and incomplete observations are available, and (b) fully online inference, which updates posterior distributions and selects designs sequentially in a computationally efficient manner. Under partial observability, dynamical systems are naturally modeled as state-space models (SSMs), where latent states mediate the link between parameters and data, making the likelihood -- and thus information-theoretic objectives like the expected information gain (EIG) -- intractable. We address these challenges by deriving new estimators of the EIG and its gradient that explicitly marginalize latent states, enabling scalable stochastic optimization in nonlinear SSMs. Our approach leverages nested particle filters for efficient online state-parameter inference with convergence guarantees. Applications to realistic models, such as the susceptible-infectious-recovered (SIR) and a moving source location task, show that our framework successfully handles both partial observability and online inference.

翻译：贝叶斯实验设计（BED）为优化数据采集提供了一个原则性框架，通过选择对未知参数信息量最大的实验。然而，现有方法无法同时应对以下两个挑战：（a）部分可观测动态系统，其中仅能获得含噪声且不完整的观测数据；（b）完全在线推断，即以计算高效的方式顺序更新后验分布并选择实验方案。在部分可观测条件下，动态系统自然被建模为状态空间模型（SSM），其中潜在状态作为参数与数据之间的中介，使得似然函数——以及诸如期望信息增益（EIG）等信息论目标——难以处理。我们通过推导新的EIG及其梯度估计量来解决这些挑战，这些估计量显式地对潜在状态进行边缘化处理，从而在非线性SSM中实现可扩展的随机优化。我们的方法利用嵌套粒子滤波器进行高效的在线状态-参数推断，并具有收敛性保证。在现实模型（如易感-感染-恢复（SIR）模型和移动源定位任务）上的应用表明，该框架成功解决了部分可观测性与在线推断的双重挑战。