# Constrained Group Relative Policy Optimization

arXiv: https://arxiv.org/abs/2602.05863 · HTML: https://mlsanity.com/paper/2602.05863/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 38 of its 55 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Placed in

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

## Builds on (most cited first, 30 of 38)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [Safe RLHF: Safe Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2310.12773/) (2023)
- [NuPlan: A closed-loop ML-based planning benchmark for autonomous vehicles](https://mlsanity.com/paper/2106.11810/) (2021)
- [Interpretable Preferences via Multi-Objective Reward Modeling and Mixture-of-Experts](https://mlsanity.com/paper/2406.12845/) (2024)
- [NAVSIM: Data-Driven Non-Reactive Autonomous Vehicle Simulation and Benchmarking](https://mlsanity.com/paper/2406.15349/) (2024)
- [Responsive Safety in Reinforcement Learning by PID Lagrangian Methods](https://mlsanity.com/paper/2007.03964/) (2020)
- [On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems](https://mlsanity.com/paper/1906.00331/) (2019)
- [Inverse Reward Design](https://mlsanity.com/paper/1711.02827/) (2017)
- [Parting with Misconceptions about Learning-based Vehicle Motion Planning](https://mlsanity.com/paper/2306.07962/) (2023)
- [GDPO: Group reward-Decoupled Normalization Policy Optimization for Multi-reward RL Optimization](https://mlsanity.com/paper/2601.05242/) (2026)
- [Pseudo-Simulation for Autonomous Driving](https://mlsanity.com/paper/2506.04218/) (2025)
- [Alpamayo-R1: Bridging Reasoning and Action Prediction for Generalizable Autonomous Driving in the Long Tail](https://mlsanity.com/paper/2511.00088/) (2025)
- [Using Natural Language for Reward Shaping in Reinforcement Learning](https://mlsanity.com/paper/1903.02020/) (2019)
- [Trial without Error: Towards Safe Reinforcement Learning via Human Intervention](https://mlsanity.com/paper/1707.05173/) (2017)
- [Confronting Reward Model Overoptimization with Constrained RLHF](https://mlsanity.com/paper/2310.04373/) (2023)
- [CoVLA: Comprehensive Vision-Language-Action Dataset for Autonomous Driving](https://mlsanity.com/paper/2408.10845/) (2024)
- [SafeVLA: Towards Safety Alignment of Vision-Language-Action Model via Constrained Learning](https://mlsanity.com/paper/2503.03480/) (2025)
- [Drive-R1: Bridging Reasoning and Planning in VLMs for Autonomous Driving with Reinforcement Learning](https://mlsanity.com/paper/2506.18234/) (2025)
- [CaRL: Learning Scalable Planning Policies with Simple Rewards](https://mlsanity.com/paper/2504.17838/) (2025)

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

- [TEMPO: Temporal Enforcement via Mode-Separated Policy Optimization for Trustworthy LLM Backtesting](https://mlsanity.com/paper/2605.18843/) (2026)
- [GPAgentBench-2K: Benchmarking Large Language Model Agents in Complex Clinical Action Space](https://mlsanity.com/paper/2608.30188/) (2026)

## Abstract (arXiv)

Group Relative Policy Optimization (GRPO) remains the dominant critic-free approach for fine-tuning LLMs and VLMs, but its compatibility with constrained policy optimization (e.g. for safety-critical domains) has not been carefully examined. In this work, we introduce Constrained GRPO, a Lagrangian-based extension of GRPO for constrained policy optimization. We show that the standard practice of scalarizing rewards before normalization introduces a critical Lagrangian-specific failure mode: GRPO's within-group normalization makes constrained optimization highly sensitive to how multi-component learning signals are aggregated. We show that scalarizing rewards before normalization introduces shared-denominator coupling, so that changing one multiplier alters not only the emphasis on its corresponding constraint, but also the relative weighting of the reward and other constraints. We address this with a simple but crucial modification: scalarizing standardized advantages rather than rewards. This yields a better-conditioned update by addressing the coupling induced by reward scalarization, resulting in better-behaved multiplier dynamics and more stable constraint enforcement in practice. Empirically, across a controlled gridworld, a real-world autonomous driving benchmark, and a mathematical reasoning task, Constrained GRPO consistently achieves better adherence to specified constraints while maintaining or improving task performance.