# Gradient Starvation in Binary-Reward GRPO: Why Group-Mean Centering Fails and Why the Simplest Fix Works

arXiv: https://arxiv.org/abs/2605.07689 · HTML: https://mlsanity.com/paper/2605.07689/

## Key facts

- Cited by 6 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 15 references that are in the map.
- First posted on arXiv 8 May 2026.

## 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)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [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)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [ExGRPO: Learning to Reason from Experience](https://mlsanity.com/paper/2510.02245/) (2025)
- [Single-stream Policy Optimization](https://mlsanity.com/paper/2509.13232/) (2025)
- [RC-GRPO: Reward-Conditioned Group Relative Policy Optimization for Multi-Turn Tool Calling Agents](https://mlsanity.com/paper/2602.03025/) (2026)

## Built on by (most cited first, 6 of 6)

- [GRPO, Dr. GRPO, and DAPO Are Three Operations on One Number: The Group-Standard-Deviation Identity](https://mlsanity.com/paper/2607.00152/) (2026)
- [Are Verifier Errors Independent Within a GRPO Group? Evidence from Qwen2.5 Rollouts](https://mlsanity.com/paper/2609.06386/) (2026)
- [DiffGate: Difficulty-Gated Teacher Guidance for On-Policy Distillation](https://mlsanity.com/paper/2610.04596/) (2026)
- [Balancing Reference Guidance and Free Generation in Trajectory Rollouts for Reasoning RL](https://mlsanity.com/paper/2610.11128/) (2026)
- [Checking the Checkers: A Synthesis of Verifier Noise and Robustness in RLVR](https://mlsanity.com/paper/2610.17824/) (2026)
- [ActICL: Post-Training for Agentic Multimodal In-Context Learning](https://mlsanity.com/paper/2610.19475/) (2026)

## Abstract (arXiv)

Group Relative Policy Optimization (GRPO) is a standard algorithm for reinforcement learning from verifiable rewards, but its group-mean-centered advantage can fail under binary rewards. The failure mode is gradient starvation: when every response in a group is correct or every response is wrong, the centered advantage is exactly zero and the policy receives no learning signal. We prove that the true degeneracy rate always exceeds the i.i.d. Bernoulli prediction by Jensen's inequality, and observe a 0.69 degeneracy rate at group size four in logged Qwen3.5-9B GSM8K training. We then show that the fixed-reference Sign advantage, A=2r-1, performs pass@G failure descent by increasing the probability that at least one sample in the group succeeds. On the full GSM8K test set across seven seeds, Sign reaches 73.8% accuracy versus 28.4% for standard normalized group-mean DrGRPO at group size four, a 45.4 point gain with p<0.0001. The effect is directionally consistent on Llama-3.1-8B and positive but underpowered on a MATH-500 transfer check. Pass@k analysis indicates that the main benefit is search compression rather than large capacity expansion, aligning the empirical gains with recent RLVR ceiling observations.