Distill-Belief: Closed-Loop Inverse Source Localization and Characterization in Physical Fields
This work addresses the challenge of balancing uncertainty estimation and computational efficiency in real-time active sensing for robotics and environmental monitoring.
Distill-Belief introduces a teacher-student framework for closed-loop inverse source localization that decouples accurate Bayesian inference from efficient control, achieving reduced sensing cost and improved accuracy across seven field modalities while mitigating reward hacking.
{Closed-loop inverse source localization and characterization (ISLC) requires a mobile agent to select measurements that localize sources and infer latent field parameters under strict time constraints.} {The core challenge lies in the belief-space objective: valid uncertainty estimation requires expensive Bayesian inference, whereas using fast learned belief model leads to reward hacking, in which the policy exploits approximation errors rather than actually reducing uncertainty.} {We propose \textbf{Distill-Belief}, a teacher--student framework that decouples correctness from efficiency. A Bayes-correct particle-filter teacher maintains the posterior and supplies a dense information-gain signal, while a compact student distills the posterior into belief statistics for control and an uncertainty certificate for stopping. At deployment, only the student is used, yielding constant per-step cost.} {Experiments on seven field modalities and two stress tests show that Distill-Belief consistently reduces sensing cost and improves success, posterior contraction, and estimation accuracy over baselines, while mitigating reward hacking.}