# DRA-GRPO: Your GRPO Needs to Know Diverse Reasoning Paths for Mathematical Reasoning

arXiv: https://arxiv.org/abs/2505.09655 · HTML: https://mlsanity.com/paper/2505.09655/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 12 of its 34 references that are in the map.
- First posted on arXiv 14 May 2025.

## Placed in

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

## Builds on (most cited first, 12 of 12)

- [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)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Reason-RFT: Reinforcement Fine-Tuning for Visual Reasoning of Vision Language Models](https://mlsanity.com/paper/2503.20752/) (2025)
- [Reinforcement Learning for Reasoning in Small LLMs: What Works and What Doesn't](https://mlsanity.com/paper/2503.16219/) (2025)
- [Reinforcement Learning Outperforms Supervised Fine-Tuning: A Case Study on Audio Question Answering](https://mlsanity.com/paper/2503.11197/) (2025)

## Built on by (most cited first, 18 of 18)

- [Group Critical-token Policy Optimization for Autoregressive Image Generation](https://mlsanity.com/paper/2509.22485/) (2025)
- [EvoTrainer: Co-Evolving LLM Policies and Training Harnesses for Autonomous Agentic Reinforcement Learning](https://mlsanity.com/paper/2606.03108/) (2026)
- [F-GRPO: Don't Let Your Policy Learn the Obvious and Forget the Rare](https://mlsanity.com/paper/2602.06717/) (2026)
- [Random Policy Valuation is Enough for LLM Reasoning with Verifiable Rewards](https://mlsanity.com/paper/2509.24981/) (2025)
- [FastGRPO: Accelerating Policy Optimization via Concurrency-aware Speculative Decoding and Online Draft Learning](https://mlsanity.com/paper/2509.21792/) (2025)
- [AceGRPO: Adaptive Curriculum Enhanced Group Relative Policy Optimization for Autonomous Machine Learning Engineering](https://mlsanity.com/paper/2602.07906/) (2026)
- [Know What You Know: Metacognitive Entropy Calibration for Verifiable RL Reasoning](https://mlsanity.com/paper/2602.22751/) (2026)
- [MMR-GRPO: Accelerating GRPO-Style Training through Diversity-Aware Reward Reweighting](https://mlsanity.com/paper/2601.09085/) (2026)
- [Are We Measuring Strategy or Phrasing? The Gap Between Surface- and Approach-Level Diversity in LLM Math Reasoning](https://mlsanity.com/paper/2606.29985/) (2026)
- [BODHI: Do LLMs Branch Out and Discover Heterogeneous Inferences?](https://mlsanity.com/paper/2608.02867/) (2026)
- [PrAg-PO: Prompt Augmented Policy Optimization for Robust and Diverse Mathematical Reasoning](https://mlsanity.com/paper/2602.03190/) (2026)
- [Smaller Models are Natural Explorers for Policy-Level Diversity in GRPO](https://mlsanity.com/paper/2605.30789/) (2026)
- [A First-Principles Derivation of LLM Policy Optimization: From Expected Reward to GRPO and Its Structural Extensions](https://mlsanity.com/paper/2606.16733/) (2026)
- [Rewarding Structural Conformance of Reasoning using Process Mining](https://mlsanity.com/paper/2510.25065/) (2025)
- [Mimic Human Cognition, Master Multi-Image Reasoning: A Meta-Action Framework for Enhanced Visual Understanding](https://mlsanity.com/paper/2601.07298/) (2026)
- [Mags-RL: Wearing Multimodal LLMs a Magnifying Glass via Agentic Reinforcement Learning For Complex Scene Reasoning](https://mlsanity.com/paper/2605.27960/) (2026)
- [ReCo: Reweighting GRPO Against Distributional Concentration](https://mlsanity.com/paper/2607.26862/) (2026)
- [Edu-QuRating: Multi-Dimensional Educational Data Curation with Distilled Pairwise Judgements](https://mlsanity.com/paper/2609.09425/) (2026)

## Abstract (arXiv)

Post-training LLMs with Reinforcement Learning, specifically Group Relative Policy Optimization (GRPO), has emerged as a paradigm for enhancing mathematical reasoning. However, standard GRPO relies on scalar correctness rewards that are often non-injective with respect to semantic content: distinct reasoning paths receive identical rewards. This leads to a Diversity-Quality Inconsistency, where the policy collapses into a narrow set of dominant modes while ignoring equally valid but structurally novel strategies. To bridge this gap, we propose Diversity-aware Reward Adjustment (DRA), a theoretically grounded framework that calibrates the reward signal using the semantic density of sampled groups. By leveraging Submodular Mutual Information (SMI), DRA implements an Inverse Propensity Scoring (IPS) mechanism that effectively de-biases the gradient estimation. This creates a repulsive force against redundancy, driving the policy to achieve better coverage of the high-reward landscape. Our method is plug-and-play and integrates seamlessly with GRPO variants. Empirical evaluations on five math benchmarks demonstrate that DRA-GRPO consistently outperforms strong baselines, achieving an average accuracy of 58.2% on DeepSeek-R1-Distill-Qwen-1.5B with only 7,000 training samples and 55 cost, highlighting the critical role of diversity calibration in data-efficient alignment. The code is available at https://github.com/xiwenc1/DRA-GRPO.