RL-ARC: Calibrating Large Reasoning Models via Reasoning-guided Uncertainty

Scaling test-time computation with reinforcement learning (RL) has emerged as a reliable path to improve large language models (LLM) reasoning ability. Yet, outcome-based reward often incentivizes models to be overconfident, leading to hallucinations, unreliable confidence-based control, and unnecessary compute allocation. We introduce Reinforcement Learning with Confidence Margin (\textbf{RLCM}), a calibration-aware RL framework that jointly optimizes correctness and confidence reliability via a margin-enhanced process reward over intermediate-budget completions. Rather than aligning confidence to correctness likelihoods, RLCM encourages to widen the confidence margin between correct and incorrect steps within a single reasoning trajectory. Across mathematical, code, logic and science benchmarks, our method substantially improves calibration while maintaining or improving accuracy. We further show that, with calibrated confidence signals, the resulting models enable more efficient conformal risk control and effective confidence-weighted aggregation.

Reasoning language models are increasingly asked not only to answer difficult questions, but also to estimate their likelihood of success. Existing methods typically elicit confidence only once: either before thinking or after answering. We argue that confidence in reasoning models is state-dependent: before thinking, confidence should estimate the chance of the model correctly solving the prompt, while after thinking it should predict whether the realized answer is likely to be correct. This distinction determines the appropriate supervision target: prompt-level success should supervise confidence estimates made after seeing the prompt, while individual answer-level correctness should supervise confidence estimates made after answering. We introduce CALIBER (Calibration Before and After Reasoning), which elicits both estimates and supervises each with the target matched to its information state. Under this unified protocol, CALIBER reduces Expected Calibration Error (ECE) by 52.5% over the strongest single-confidence baseline on BigMathDigits for the 7B model, while achieving the best Brier score and AUROC, and remains within 2.1 points of the best accuracy. Further, on a larger 30B model, CALIBER achieves the best ECE on BigMathDigits while remaining competitive in Brier score and AUROC. Out of distribution, it achieves the best ECE and Brier score on GPQA and TriviaQA, and remains competitive on SimpleQA. Ablations further show that this position-target alignment is most beneficial under distribution shift where it consistently reduces calibration error across all out-of-distribution benchmarks.

Reinforcement learning with verifiable rewards (RLVR) trains reasoning models to produce correct answers, but does not ensure that their stated confidence is calibrated. The resulting models are systematically overconfident. Recent methods train calibration inside the RLVR loop by having the model state a numerical confidence alongside its answer, but they all obtain the confidence by sampling it as text. This choice imposes two costs: a sampled confidence introduces variance and in practice collapses to a handful of distinct values, and sampling makes the confidence non-differentiable, forcing the calibration loss through a scalar reward. We propose CREDO (Confidence REaDOut) to replace sampling with a deterministic readout. While RLVR optimizes correctness, CREDO reads the confidence from a dedicated token pair in the model's output distribution and trains it by differentiable regression. CREDO further turns the trained confidence into a signal for accuracy, weighting rollouts by how far confidence and outcome disagree, so that accuracy and calibration improve together. Across mathematical and code reasoning, CREDO attains the best accuracy and calibration, and the gains extend to abstention and selective prediction.