# CorrGRPO: Correlation-Normalized GRPO for Multi-Reward Learning

arXiv: https://arxiv.org/abs/2609.36820 · HTML: https://mlsanity.com/paper/2609.36820/

## 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 24 of its 26 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Placed in

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

## Builds on (most cited first, 24 of 24)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [Safe RLHF: Safe Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2310.12773/) (2023)
- [API-Bank: A Comprehensive Benchmark for Tool-Augmented LLMs](https://mlsanity.com/paper/2304.08244/) (2023)
- [InjecAgent: Benchmarking Indirect Prompt Injections in Tool-Integrated Large Language Model Agents](https://mlsanity.com/paper/2403.02691/) (2024)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Agent Security Bench (ASB): Formalizing and Benchmarking Attacks and Defenses in LLM-based Agents](https://mlsanity.com/paper/2410.02644/) (2024)
- [ToolRL: Reward is All Tool Learning Needs](https://mlsanity.com/paper/2504.13958/) (2025)
- [MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention](https://mlsanity.com/paper/2506.13585/) (2025)
- [GDPO: Group reward-Decoupled Normalization Policy Optimization for Multi-reward RL Optimization](https://mlsanity.com/paper/2601.05242/) (2026)
- [AgentDojo: A Dynamic Environment to Evaluate Prompt Injection Attacks and Defenses for LLM Agents](https://mlsanity.com/paper/2406.13352/) (2024)
- [LeetCodeDataset: A Temporal Dataset for Robust Evaluation and Efficient Training of Code LLMs](https://mlsanity.com/paper/2504.14655/) (2025)
- [Learning to Optimize Multi-Objective Alignment Through Dynamic Reward Weighting](https://mlsanity.com/paper/2509.11452/) (2025)
- [MO-GRPO: Mitigating Reward Hacking of Group Relative Policy Optimization on Multi-Objective Problems](https://mlsanity.com/paper/2509.22047/) (2025)
- [Multi-objective Reinforcement learning from AI Feedback](https://mlsanity.com/paper/2406.07295/) (2024)
- [Multi-Objective and Mixed-Reward Reinforcement Learning via Reward-Decorrelated Policy Optimization](https://mlsanity.com/paper/2605.13641/) (2026)

## Abstract (arXiv)

Group Relative Policy Optimization (GRPO) is widely used to train reasoning language models, where it computes advantages by centering and normalizing rewards across rollouts of the same prompt. For multiple rewards, GRPO sums the reward components and normalizes the total reward by its within-group standard deviation. The corresponding variance equals the sum of all pairwise reward covariances. For a fixed centered reward, larger aggregate covariance produces smaller advantages, and vice versa, allowing update magnitudes to adapt to reward dependence. However, correlated rewards with large scales can dominate this normalization and suppress signals from smaller-scale rewards. We propose Correlation-Normalized GRPO (CorrGRPO), which normalizes pairwise covariances into Pearson correlation coefficients. CorrGRPO keeps the centered total reward unchanged while balancing the influence of differently scaled rewards on the correlation-based normalization. This allows advantage magnitudes to adapt to reward correlations without the normalization being dominated by large-scale reward components. We compare CorrGRPO with GRPO and other variants on code generation, tool calling, and agent security, using models ranging from 0.5B to 8B parameters. These tasks all involve multiple rewards that can improve together or present tradeoffs. Results show improvements across three domains, including code generation, tool calling, and agent security. Our code is available at https://github.com/HKUST-KnowComp/CorrGRPO.