# GRPO-LEAD: A Difficulty-Aware Reinforcement Learning Approach for Concise Mathematical Reasoning in Language Models

arXiv: https://arxiv.org/abs/2504.09696 · HTML: https://mlsanity.com/paper/2504.09696/

## Key facts

- Cited by 82 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 13 of its 21 references that are in the map.
- First posted on arXiv 13 Apr 2025.

## Placed in

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

## Builds on (most cited first, 13 of 13)

- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Demystifying Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2502.03373/) (2025)
- [Light-R1: Curriculum SFT, DPO and RL for Long COT from Scratch and Beyond](https://mlsanity.com/paper/2503.10460/) (2025)
- [GPG: A Simple and Strong Reinforcement Learning Baseline for Model Reasoning](https://mlsanity.com/paper/2504.02546/) (2025)
- [Reinforcement Learning with a Corrupted Reward Channel](https://mlsanity.com/paper/1705.08417/) (2017)
- [Optimizing Safe and Aligned Language Generation: A Multi-Objective GRPO Approach](https://mlsanity.com/paper/2503.21819/) (2025)

## Built on by (most cited first, 30 of 82)

- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [Between Underthinking and Overthinking: An Empirical Study of Reasoning Length and correctness in LLMs](https://mlsanity.com/paper/2505.00127/) (2025)
- [Geometric-Mean Policy Optimization](https://mlsanity.com/paper/2507.20673/) (2025)
- [SEED-GRPO: Semantic Entropy Enhanced GRPO for Uncertainty-Aware Policy Optimization](https://mlsanity.com/paper/2505.12346/) (2025)
- [Learning When to Think: Shaping Adaptive Reasoning in R1-Style Models via Multi-Stage RL](https://mlsanity.com/paper/2505.10832/) (2025)
- [Part I: Tricks or Traps? A Deep Dive into RL for LLM Reasoning](https://mlsanity.com/paper/2508.08221/) (2025)
- [ExGRPO: Learning to Reason from Experience](https://mlsanity.com/paper/2510.02245/) (2025)
- [Search and Refine During Think: Facilitating Knowledge Refinement for Improved Retrieval-Augmented Reasoning](https://mlsanity.com/paper/2505.11277/) (2025)
- [Reflect, Retry, Reward: Self-Improving LLMs via Reinforcement Learning](https://mlsanity.com/paper/2505.24726/) (2025)
- [Promoting Efficient Reasoning with Verifiable Stepwise Reward](https://mlsanity.com/paper/2508.10293/) (2025)
- [Difficulty-Aware Agentic Orchestration for Query-Specific Multi-Agent Workflows](https://mlsanity.com/paper/2509.11079/) (2025)
- [Learning to Optimize Multi-Objective Alignment Through Dynamic Reward Weighting](https://mlsanity.com/paper/2509.11452/) (2025)
- [GRPO-λ: Credit Assignment improves LLM Reasoning](https://mlsanity.com/paper/2510.00194/) (2025)
- [Demystifying Group Relative Policy Optimization: Its Policy Gradient is a U-Statistic](https://mlsanity.com/paper/2603.01162/) (2026)
- [Harder Is Better: Boosting Mathematical Reasoning via Difficulty-Aware GRPO and Multi-Aspect Question Reformulation](https://mlsanity.com/paper/2601.20614/) (2026)
- [Does Your Reasoning Model Implicitly Know When to Stop Thinking?](https://mlsanity.com/paper/2602.08354/) (2026)
- [SATORI-R1: Incentivizing Multimodal Reasoning through Explicit Visual Anchoring](https://mlsanity.com/paper/2505.19094/) (2025)
- [DisCO: Reinforcing Large Reasoning Models with Discriminative Constrained Optimization](https://mlsanity.com/paper/2505.12366/) (2025)
- [Alignment and Safety in Large Language Models: Safety Mechanisms, Training Paradigms, and Emerging Challenges](https://mlsanity.com/paper/2507.19672/) (2025)
- [Devil is in Narrow Policy: Unleashing Exploration in Driving VLA Models](https://mlsanity.com/paper/2603.06049/) (2026)
- [Self-Compression of Chain-of-Thought via Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2601.21919/) (2026)
- [Semantically-Aware Rewards for Open-Ended R1 Training in Free-Form Generation](https://mlsanity.com/paper/2506.15068/) (2025)
- [MAPO: Mixed Advantage Policy Optimization](https://mlsanity.com/paper/2509.18849/) (2025)
- [Supervised Reinforcement Learning: From Expert Trajectories to Step-wise Reasoning](https://mlsanity.com/paper/2510.25992/) (2025)
- [PAPO: Stabilizing Rubric Integration Training via Decoupled Advantage Normalization](https://mlsanity.com/paper/2603.26535/) (2026)
- [Decomposing Elements of Problem Solving: What "Math" Does RL Teach?](https://mlsanity.com/paper/2505.22756/) (2025)
- [SEM: Reinforcement Learning for Search-Efficient Large Language Models](https://mlsanity.com/paper/2505.07903/) (2025)
- [Generate, Filter, Control, Replay: A Comprehensive Survey of Rollout Strategies for LLM Reinforcement Learning](https://mlsanity.com/paper/2605.02913/) (2026)
- [Unlocking the Potential of Difficulty Prior in RL-based Multimodal Reasoning](https://mlsanity.com/paper/2505.13261/) (2025)

## Abstract (arXiv)

Group Relative Policy Optimization (GRPO), which is widely adopted by R1-like reasoning models, has advanced mathematical reasoning. Nevertheless, GRPO faces challenges in reward sparsity, verbosity, and inadequate focus on problem difficulty. We propose GRPO-LEAD, enhancing GRPO with: (1) length-regularized rewards to encourage conciseness while maintaining accuracy; (2) explicit penalties for incorrect solutions to improve model precision; and (3) difficulty-aware advantage reweighting for robust generalization on challenging problems. Comprehensive evaluations demonstrate that GRPO-LEAD significantly improves reasoning accuracy, conciseness, and efficiency. Our approach achieves state-of-the-art performance for 14B-scale models, underscoring the synergy of our methods with appropriate model scale and high-quality data. Our source code, generated dataset, and models are available at https://github.com/aeroplanepaper/GRPO-LEAD.