Beyond GRPO and On-Policy Distillation: An Empirical Sparse-to-Dense Reward Principle for Language-Model Post-Training

When labeled verifiable training data is scarce, each checked example should be used where it has the most value. A common approach is to train the deployment student model directly with sparse RL methods such as GRPO. We argue that this is often inefficient. Sparse sequence-level reward is most useful for strong models that can explore and discover better behavior, while dense token-level teacher supervision is better suited for compressing that behavior into a smaller student. This suggests a simple allocation rule: use scarce labeled data upstream to improve the strongest available teacher, then transfer the improved behavior downstream through dense supervision. In this view, GRPO-style sparse RL and OPD-style distillation are not competing methods, but two reward-density regimes used at different stages. We evaluate this rule on verifiable math tasks with Qwen3 and Llama models. For a fixed Qwen3-1.7B deployment student, distilling from an RL-improved 8B teacher outperforms applying GRPO directly to the student with the same labeled data. In contrast, distilling from the same teacher before RL gives weaker results. The transfer bridge is also important: a forward-KL warmup on teacher rollouts followed by OPD on student rollouts performs best on MATH before any later student-side sparse RL, and gives the strongest pre-Stage 3 AIME results for the canonical 8B and 14B teachers. Finally, the bridge makes later student-side RL more effective. GRPO is weak when applied to a cold student, but after the bridge it raises MATH accuracy from 75.4% to 78.5%, outperforming a matched replay control by 2.8 points. Overall, the lesson is to avoid spending scarce labeled data on the least prepared policy: use sparse reward for teacher-side discovery, dense transfer for student compression, and student-side sparse reward only after the student has been bridged.