When Does Calibration Matter for Safe Model Routing? Conformal Risk Control Under Imperfect Gate Calibration

Iqtedar Uddin, Mazin Khider, André Bauer

Keywords: Conformal Risk Control, Probability Calibration, Distribution-Free Inference, Model Routing, Calibration-Efficiency Separation, Post-hoc Calibration

Abstract: In safety-critical or regulated deployments, practitioners often wish to use simpler or interpretable surrogate models that approximate a more accurate but expensive black-box model, yet lack formal guarantees of when they are sufficiently accurate. Model routing addresses this by deciding, for each input, whether a surrogate can safely replace the expensive model without degrading predictions beyond a tolerance $\tau$. A lightweight classifier (the gate) predicts from input features alone whether the surrogate is safe. A conformal procedure based on Clopper--Pearson bounds then selects a routing threshold on held-out data, guaranteeing that the violation rate among routed inputs is at most $\alpha$ with probability $1-\delta$. We establish a formal separation between probabilistic calibration and distribution-free safety. While conformal thresholding guarantees validity regardless of the gate's Expected Calibration Error (ECE), we empirically demonstrate that applying post-hoc calibration (e.g., Beta scaling) stabilizes the conformal procedure. Calibration selectively filters borderline instances, reducing empirical violation rates closer to the target nominal level across 35 OpenML datasets, and yields a highly interpretable routing threshold.

Submission Number: 13