Calibrated Preference Learning: The Case of Label Ranking

When providing forecasted probabilities with a predictive model, the ideal model offers perfect calibration: the true probability of the outcome (i.e., the probability that $Y=1$) exactly matches the forecasted probability $f(X)$. In practice, models inevitably exhibit calibration error, and it is therefore important to be able to measure this miscalibration to assess a model's reliability. The Expected Calibration Error (ECE) is the most widely used measure of miscalibration, but is known to be impossible to estimate the ECE with guaranteed accuracy in an assumption-free setting. In this work, we propose an alternative measure, the rankECE, that is based on comparing points with neighboring values of the predicted probability $f(X)$. Our theoretical guarantees and empirical results establish that rankECE provides a better proxy for ECE as compared to binned approximations to ECE, which are the most commonly-used approximations in practice.

Reinforcement learning post-training has substantially improved the reasoning accuracy of vision-language models, yet the resulting policies remain poorly calibrated. Terminal correctness rewards provide no gradient that penalizes confident errors more than uncertain ones and no signal that ties confidence to the quality of visual evidence, a gap that becomes especially severe under corrupted or ambiguous inputs where models continue to report high confidence on incorrect answers. We introduce Ranking-Aware Calibration (RAC), a training-time framework that supervises confidence using two comparison signals that group-based RL already produces at no additional labeling cost. The ranking-aware group loss enforces that a better rollout receives higher confidence than a worse one within the same prompt. The clean--corrupted pairwise loss enforces that confidence attenuates as visual evidence degrades. Because the ranking signal forces the policy to distinguish between correct and incorrect reasoning paths, it also reinforces task accuracy beyond what correctness rewards alone produce. Both losses require no external confidence annotations and integrate naturally with group-based RL post-training. We instantiate RAC on Qwen2.5-VL and InternVL-3.5 backbones and evaluate on six multimodal reasoning benchmarks under clean and corrupted inputs. Empirical results show that the ranking-aware loss substantially improves task accuracy by teaching the policy to discriminate between better and worse reasoning, while the pairwise corruption loss reduces calibration error under degraded inputs. Their combination achieves the best calibration across all tested backbones while improving accuracy in the majority of settings.

Web search, product search, and question-answering retrieval systems often assign a relevance label and confidence score to each query-candidate pair. The relevance label describes how well a page, product, or passage matches the query, while the confidence often guides downstream use or fallback decisions. Post-hoc calibration is therefore needed because misaligned confidence can make systems over-trust wrong predictions or unnecessarily defer correct ones. However, calibration mainly aligns confidence with average correctness, and does not remove predicted-label-dependent reliability differences that remain within the same calibrated confidence level. We address this gap with Label-wise Monotone Reliability Projection (MRP), which learns label-wise monotone functions that map calibrated confidence to correctness reliability while preserving the original predicted labels and class probabilities. The resulting reliability score reranks fixed predictions according to residual risk. Across six information access relevance datasets and multiple post-hoc calibrators, MRP improves reliability reranking and average fallback utility while preserving full-coverage accuracy and ECE. Structural ablations show that the main gains come from label-wise residual reliability rather than from global confidence remapping. We further analyze when MRP reliability scores can be embedded back into top-label probability geometry, showing that this projection is useful as a compatibility analysis but is distinct from the main reliability-reranking objective. The implementation will be made publicly available.