The Capability Frontier of GRPO

Group Relative Policy Optimization (GRPO) is widely used to post-train reasoning language models, and its rollout group size $G$ is typically treated as a compute hyperparameter. We argue that $G$ also sets a difficulty threshold below which prompts produce no learning signal. Under binary verifier rewards, a rollout group only produces a learning signal when it contains both a success and a failure, and the rate at which a prompt yields such mixed groups turns on sharply near $p_c\simeq\ln 2/G$. Below that threshold the prompt is invisible to the relative-advantage estimator regardless of optimizer state. We verify this gate directly in pass@256 rollout traces from Qwen3-1.7B, Qwen3-8B, and Llama-3.1-8B, where empirical mixed-group rates match the binomial prediction within $1.4$–$1.9$ percentage points on average per model. Sweeping fixed-$G$ GRPO with $G\in\{8,16,32,64,128\}$ then shows that difficulty-binned per-prompt improvement after training tracks the frontier shape with binned $R^2$ between $0.962$ and $0.984$ across all three model families. Treating $p_c$ as a moving target, we instantiate a frontier-tracking group-size schedule that improves the best fixed-$G$ baseline by $4.2$–$5.3$ points on MATH-500 and $2.4$–$3.4$ points on GSM8K under matched rollout budget. Ablations attribute the gain primarily to frontier-aware switch timing.