# Range-GRPO: Policy Optimization via Pairwise Relations among Reward Intervals

arXiv: https://arxiv.org/abs/2610.01548 · HTML: https://mlsanity.com/paper/2610.01548/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 34 of its 44 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Placed in

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

## Builds on (most cited first, 30 of 34)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [RLAIF vs. RLHF: Scaling Reinforcement Learning from Human Feedback with AI Feedback](https://mlsanity.com/paper/2309.00267/) (2023)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Dynabench: Rethinking Benchmarking in NLP](https://mlsanity.com/paper/2104.14337/) (2021)
- [Justice or Prejudice? Quantifying Biases in LLM-as-a-Judge](https://mlsanity.com/paper/2410.02736/) (2024)
- [Rubrics as Rewards: Reinforcement Learning Beyond Verifiable Domains](https://mlsanity.com/paper/2507.17746/) (2025)
- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [LiveBench: A Challenging, Contamination-Limited LLM Benchmark](https://mlsanity.com/paper/2406.19314/) (2024)
- [Learning to Reason without External Rewards](https://mlsanity.com/paper/2505.19590/) (2025)
- [The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning](https://mlsanity.com/paper/2505.15134/) (2025)
- [General-Reasoner: Advancing LLM Reasoning Across All Domains](https://mlsanity.com/paper/2505.14652/) (2025)
- [Style Over Substance: Evaluation Biases for Large Language Models](https://mlsanity.com/paper/2307.03025/) (2023)
- [Breaking the Exploration Bottleneck: Rubric-Scaffolded Reinforcement Learning for General LLM Reasoning](https://mlsanity.com/paper/2508.16949/) (2025)
- [First SFT, Second RL, Third UPT: Continual Improving Multi-Modal LLM Reasoning via Unsupervised Post-Training](https://mlsanity.com/paper/2505.22453/) (2025)
- [Analyzing Uncertainty of LLM-as-a-Judge: Interval Evaluations with Conformal Prediction](https://mlsanity.com/paper/2509.18658/) (2025)
- [BAGEN: Are LLM Agents Budget-Aware?](https://mlsanity.com/paper/2606.00198/) (2026)
- [TempR1: Improving Temporal Understanding of MLLMs via Temporal-Aware Multi-Task Reinforcement Learning](https://mlsanity.com/paper/2512.03963/) (2025)
- [TraPO: A Semi-Supervised Reinforcement Learning Framework for Boosting LLM Reasoning](https://mlsanity.com/paper/2512.13106/) (2025)
- [Uncertainty-Aware Reward Modeling for Stable RLHF](https://mlsanity.com/paper/2606.19818/) (2026)

## Abstract (arXiv)

As the use of large language models (LLMs) expands, post-training has become increasingly important for adapting them to downstream tasks. However, obtaining reliable supervision remains costly, especially in domains without reference answers or executable verifiers. LLM-as-a-Judge provides scalable pseudo-rewards for unlabeled responses, but a single point score does not explicitly represent reward uncertainty. This motivates representing pseudo-rewards as conformally calibrated reward ranges. We propose Range-GRPO, a semi-supervised post-training framework that combines limited labeled data with unlabeled prompts. In Group Relative Policy Optimization (GRPO), learning signals depend on relative reward comparisons within each rollout group. The proposed objective compares reward ranges pairwise rather than reducing them to point rewards, allowing interval uncertainty to affect both the magnitude and direction of these signals. Our theoretical analysis characterizes this distinction and shows that the proposed objective recovers the Dr.GRPO advantage when all reward ranges collapse to points. Empirically, Range-GRPO achieves the highest in-distribution and out-of-distribution average performance among the evaluated semi-supervised methods while requiring fewer training resources.