# Calibration-Aware Policy Optimization for Reasoning LLMs

arXiv: https://arxiv.org/abs/2604.12632 · HTML: https://mlsanity.com/paper/2604.12632/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 28 of its 49 references that are in the map.
- First posted on arXiv 14 Apr 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 28 of 28)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Why Language Models Hallucinate](https://mlsanity.com/paper/2509.04664/) (2025)
- [Beyond Binary Rewards: Training LMs to Reason About Their Uncertainty](https://mlsanity.com/paper/2507.16806/) (2025)
- [On Verbalized Confidence Scores for LLMs](https://mlsanity.com/paper/2412.14737/) (2024)
- [Learning to Route LLMs with Confidence Tokens](https://mlsanity.com/paper/2410.13284/) (2024)
- [When to Trust LLMs: Aligning Confidence with Response Quality](https://mlsanity.com/paper/2404.17287/) (2024)
- [Uncertainty Quantification for LLMs through Minimum Bayes Risk: Bridging Confidence and Consistency](https://mlsanity.com/paper/2502.04964/) (2025)
- [CDE: Curiosity-Driven Exploration for Efficient Reinforcement Learning in Large Language Models](https://mlsanity.com/paper/2509.09675/) (2025)
- [Restoring Calibration for Aligned Large Language Models: A Calibration-Aware Fine-Tuning Approach](https://mlsanity.com/paper/2505.01997/) (2025)
- [Uncalibrated Reasoning: GRPO Induces Overconfidence for Stochastic Outcomes](https://mlsanity.com/paper/2508.11800/) (2025)
- [LLM-Powered Multi-Agent System for Automated Crypto Portfolio Management](https://mlsanity.com/paper/2501.00826/) (2025)
- [Bridging Internal Probability and Self-Consistency for Effective and Efficient LLM Reasoning](https://mlsanity.com/paper/2502.00511/) (2025)
- [Beyond the Sampled Token: Preserving Candidate Support in RLVR](https://mlsanity.com/paper/2510.14807/) (2025)
- [Thinking Out Loud: Do Reasoning Models Know When They're Right?](https://mlsanity.com/paper/2504.06564/) (2025)
- [Benchmarking Deep AUROC Optimization: Loss Functions and Algorithmic Choices](https://mlsanity.com/paper/2203.14177/) (2022)
- [Towards Agents That Know When They Don't Know: Uncertainty as a Control Signal for Structured Reasoning](https://mlsanity.com/paper/2509.02401/) (2025)
- [C2GSPG: Confidence-calibrated Group Sequence Policy Gradient towards Self-aware Reasoning](https://mlsanity.com/paper/2509.23129/) (2025)
- [Entropy-Based Adaptive Weighting for Self-Training](https://mlsanity.com/paper/2503.23913/) (2025)
- [Bi-directional Model Cascading with Proxy Confidence](https://mlsanity.com/paper/2504.19391/) (2025)

## Built on by (most cited first, 5 of 5)

- [Beyond SFT-to-RL: Pre-alignment via Black-Box On-Policy Distillation for Multimodal RL](https://mlsanity.com/paper/2604.28123/) (2026)
- [Advantage Scale Calibration Imbalance in Group-Relative Optimization under Low-Variance Rewards: Diagnosis and Bounded Recovery](https://mlsanity.com/paper/2609.19164/) (2026)
- [Beyond Verbalized Confidence: Calibrating Reasoners with Differentiable Readouts](https://mlsanity.com/paper/2609.34857/) (2026)
- [OmniMed-Jev: Calibrating LVLM Confidence for Trustworthy Medical Multimodal Decisions via System One](https://mlsanity.com/paper/2610.00381/) (2026)
- [Can an Agent Learn to Predict Its Own Failure? Outcome-Grounded Confidence Calibration in LLM Agents](https://mlsanity.com/paper/2610.18614/) (2026)

## Abstract (arXiv)

Group Relative Policy Optimization (GRPO) enhances LLM reasoning but often induces overconfidence, where incorrect responses yield lower perplexity than correct ones, degrading relative calibration as described by the Area Under the Curve (AUC). Existing approaches either yield limited improvements in calibration or sacrifice gains in reasoning accuracy. We first prove that this degradation in GRPO-style algorithms stems from their uncertainty-agnostic advantage estimation, which inevitably misaligns optimization gradients with calibration. This leads to improved accuracy at the expense of degraded calibration. We then propose Calibration-Aware Policy Optimization (CAPO). It adopts a logistic AUC surrogate loss that is theoretically consistent and admits regret bound, enabling uncertainty-aware advantage estimation. By further incorporating a noise masking mechanism, CAPO achieves stable learning dynamics that jointly optimize calibration and accuracy. Experiments on multiple mathematical reasoning benchmarks show that CAPO-1.5B significantly improves calibration by up to 15% while achieving accuracy comparable to or better than GRPO, and further boosts accuracy on downstream inference-time scaling tasks by up to 5%. Moreover, when allowed to abstain under low-confidence conditions, CAPO achieves a Pareto-optimal precision-coverage trade-off, highlighting its practical value for hallucination mitigation.