# On the effectiveness of reward functions in reinforcement learning for confidence calibration of large language models

arXiv: https://arxiv.org/abs/2607.04332 · HTML: https://mlsanity.com/paper/2607.04332/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 41 references that are in the map.
- First posted on arXiv 5 Jul 2026.

## Builds on (most cited first, 23 of 23)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [RL's Razor: Why Online Reinforcement Learning Forgets Less](https://mlsanity.com/paper/2509.04259/) (2025)
- [Beyond Binary Rewards: Training LMs to Reason About Their Uncertainty](https://mlsanity.com/paper/2507.16806/) (2025)
- [Big-Math: A Large-Scale, High-Quality Math Dataset for Reinforcement Learning in Language Models](https://mlsanity.com/paper/2502.17387/) (2025)
- [SaySelf: Teaching LLMs to Express Confidence with Self-Reflective Rationales](https://mlsanity.com/paper/2405.20974/) (2024)
- [Rewarding Doubt: A Reinforcement Learning Approach to Calibrated Confidence Expression of Large Language Models](https://mlsanity.com/paper/2503.02623/) (2025)
- [It Takes Two: Your GRPO Is Secretly DPO](https://mlsanity.com/paper/2510.00977/) (2025)
- [Outcome-based Reinforcement Learning to Predict the Future](https://mlsanity.com/paper/2505.17989/) (2025)
- [Uncalibrated Reasoning: GRPO Induces Overconfidence for Stochastic Outcomes](https://mlsanity.com/paper/2508.11800/) (2025)
- [Trace Length is a Simple Uncertainty Signal in Reasoning Models](https://mlsanity.com/paper/2510.10409/) (2025)
- [Mitigating LLM Hallucination via Behaviorally Calibrated Reinforcement Learning](https://mlsanity.com/paper/2512.19920/) (2025)
- [Firm or Fickle? Evaluating Large Language Models Consistency in Sequential Interactions](https://mlsanity.com/paper/2503.22353/) (2025)
- [Know When You're Wrong: Aligning Confidence with Correctness for LLM Error Detection](https://mlsanity.com/paper/2603.06604/) (2026)
- [Consistency of Large Reasoning Models Under Multi-Turn Attacks](https://mlsanity.com/paper/2602.13093/) (2026)
- [Confidence Before Answering: A Paradigm Shift for Efficient LLM Uncertainty Estimation](https://mlsanity.com/paper/2603.05881/) (2026)

## Built on by (most cited first, 2 of 2)

- [On the Pitfalls of Verbalized Confidence Priors for Calibrating Large Reasoning Models](https://mlsanity.com/paper/2609.32470/) (2026)
- [OmniMed-Jev: Calibrating LVLM Confidence for Trustworthy Medical Multimodal Decisions via System One](https://mlsanity.com/paper/2610.00381/) (2026)

## Abstract (arXiv)

In this paper, we consider the setting where large language models (LLMs) are trained using reinforcement learning (RL) to simultaneously improve reasoning accuracy and verbalize their confidence. Our reward scheme uses two functions for rewarding confidence verbalized by the LLM: one for correct answers and the other for incorrect answers. If poorly designed, such a scheme may incentivize an LLM to answer incorrectly in order for its confidence to be calibrated, a phenomenon we term confidence reward hacking. We introduce the notion of non-hackable confidence reward schemes and provide methods for constructing them. We show that selective confidence reward hacking can arise in practical datasets under hackable reward schemes while non-hackable reward schemes are resistant to hacking. Finally, we place some of these schemes along an overconfidence-underconfidence spectrum for RL-based confidence calibration and demonstrate experimentally that they tend to exhibit the corresponding calibration biases relative to other schemes in the spectrum. The code of our experiments is available in https://anonymous.4open.science/r/rl-confidence-calibration-9ED4/README.md.