Online Bayesian Experimental Design for Partially Observed Dynamical Systems

TL;DR

This work addresses Bayesian adaptive design for partially observable dynamical systems by deriving EIG estimators and gradients that marginalize latent states, enabling online, gradient-based design. The authors integrate nested particle filters to jointly infer states and parameters online, achieving linear-time scaling and providing consistency guarantees. The BAD-PODS framework combines these estimators with online SGD to optimize continuous designs while updating the posterior via an online NPF, demonstrated on two realistic tasks (a two-group SIR model and moving-source localization). The results show that online adaptation substantially improves information gain and design quality compared to random or static designs, with practical implications for adaptive experiments in complex dynamical settings.

Abstract

Bayesian experimental design (BED) provides a principled framework for optimizing data collection, but existing approaches do not apply to crucial real-world settings such as dynamical systems with partial observability, where only noisy and incomplete observations are available. These 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. In addition, the dynamical nature of the system requires online algorithms that update posterior distributions and select designs sequentially in a computationally efficient manner. 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 (NPFs) for efficient online inference with convergence guarantees. Applications to realistic models, such as the susceptible-infected-recovered (SIR) and a moving source location task, show that our framework successfully handles both partial observability and online computation.

Figures (5)

• Figure 1: Two-group sir: differences in TEIG (ours minus baseline). Boxplots (median and interquartiles) compare BAD-PODS with random designs (left, green) and static bed (right, orange). Higher values indicate better performance for BAD-PODS.
• Figure 2: Distribution of design component $\xi_t^{(1)}$ across seeds and time (boxplots: median and interquartiles). BAD-PODS allocates more effort to group 1, which contains the unknown parameters.
• Figure 3: Example trajectory of the moving source for $t\!=\!50$ (blue line with markers) together with fixed sensor locations (red triangles).
• Figure 4: Moving source location: differences in TEIG (ours minus baseline). Boxplots (median and interquartiles) compare BAD-PODS with random designs (left, green) and static bed (right, orange). Higher values indicate better performance for BAD-PODS.
• Figure 5: Pointing error (in degrees) of sensor orientations relative to the target at selected time steps. Boxplots (median and interquartiles) show the distribution across seeds and sensors for our method, random design, and static bed approach. Lower values correspond to higher orientation accuracy.

Theorems & Definitions (1)

• Theorem 1