arXiv:2605.19557v2 Announce Type: replace Abstract: We study post-hoc Learning to Defer (L2D) through the lens of ideal distributions: divergence-regularized reweightings of the data distribution under which a model attains low task loss. We define deferral via the density-ratio between a model's and an expert's ideals. Using the reduction from density-ratio estimation to class-probability estimation, we derive the DR CPE losses for post-hoc L2D scorers. Deferral decisions are then made by thresholding the scorer. For KL-based ideal distributions, our deferral rule recovers Chow's rule under the original distribution and a connection to an expert-tilted Bayes posterior---which incorporates the expert's performance---depending on if the ideal distributions are marginal or joint distributions. This leads to two variants of the DR CPE losses, with the joint variant being computationally convenient in practice. We establish consistency properties of the joint DR CPE losses when considering the zero-one task loss and strongly proper composite CPE losses. Experimentally, our approach is competitive compared to common baselines and is more robust across dataset settings. More broadly, our results cast post-hoc L2D as density-ratio estimation between ideal distributions, bridging Chow-style rules, expert comparison, and elucidating connections to related learning settings including anomaly detection.