Distill-Belief: Closed-Loop Inverse Source Localization and Characterization in Physical Fields

TL;DR

Distill-Belief introduces a teacher-student framework for efficient closed-loop source localization that reduces sensing costs and mitigates reward hacking by decoupling correctness from efficiency.

Contribution

The paper presents a novel framework that separates accurate Bayesian inference from control efficiency, enabling effective source localization with lower costs and improved robustness.

Findings

Distill-Belief reduces sensing costs across seven field modalities.

It improves success rates, posterior contraction, and estimation accuracy.

The method mitigates reward hacking compared to baselines.

Abstract

{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.}