Distributional, margin-free estimation-error guarantee

Derive a distributional guarantee for the EIG-Cost policy that controls the effect of CVAE, classifier, and Monte Carlo estimation errors without assuming a positive decision margin along the exact greedy trajectory.

Background

The paper’s stability theorem guarantees that approximate EIG-Cost makes exactly the same decisions as the exact greedy policy when estimation errors are uniformly bounded and every decision has a margin exceeding twice that error.

The result is conditional on margins along the realized trajectory. The authors explicitly identify the absence of a distributional guarantee that remains valid when margins are small as an unresolved problem.

References

The stability guarantee (Theorem~\ref{thm:stability}) is conditional on a margin condition holding along the trajectory; it certifies that estimation error changes no acquisition decision when decisions have margin, but gives no bound when margins are small, and a distributional (margin-free) guarantee remains open.

— The Lagrangian Structure of Cost-Penalized Active Feature Acquisition  (2610.21919 - Bingham, 15 Oct 2026) in Limitations, Section 7 (Discussion)