这篇论文为资源受限的团队提供了明确的训练策略——用最强模型做探索、用小模型做部署，做模型压缩或后训练的开发者可以直接参考这个稀疏到稠密的分配原则来提升效率。
该论文提出了一种新的语言模型后训练原则：将稀缺的标注验证数据优先用于最强模型（教师）进行稀疏奖励强化学习（如GRPO），然后通过稠密奖励蒸馏（如OPD）将行为迁移到小模型（学生）。实验表明，在固定学生模型大小（Qwen3-1.7B）下，先对8B教师进行RL再蒸馏，效果优于直接在学生上运行GRPO。该原则强调避免在未准备好的策略上使用稀缺数据，而是通过“稀疏奖励发现→稠密迁移→学生侧稀疏奖励”的流程优化资源分配。
Beyond GRPO and On-Policy Distillation: An Empirical Sparse-to-Dense Reward Principle for Language-Model Post-Training
In settings where labeled verifiable training data is the binding constraint, each checked example should be allocated carefully. The standard practice is to use this data directly on the model that will be deployed, for example by running GRPO on the deployment student. We argue that this is often an inefficient allocation because it overlooks a reward-density principle: sparse sequence-level reward should train models where exploration is productive, while dense token-level teacher reward should be used where the aim is to compress behavior into a smaller model. In this view, GRPO-style sparse RL and OPD-style dense teacher supervision are not separate recipes; they are different reward-density regimes. The allocation rule is simple: use scarce labeled training data upstream on the strongest model that can turn it into reward-shaped behavior, then transfer that behavior downstream as dense supervision. We evaluate this rule on verifiable math with Qwen3 and Llama models. At fixed Qwen3-1.7B deployment-student size, an RL-improved 8B teacher distilled through the dense bridge outperforms direct GRPO on the same student, while transfer from the same teacher before RL underperforms. The bridge is important: a forward-KL warmup on teacher rollouts followed by OPD on student rollouts is consistently strongest on MATH before any post-bridge student-side sparse RL, and also gives the best pre-Stage~3 AIME endpoints for the canonical 8B/14B teachers. The bridge also makes later student-side sparse RL effective: GRPO that is weak on a cold student lifts MATH from $75.4\%$ to $78.5\%$ after the bridge and outperforms a matched replay control by $2.8$ points. The operational principal is to avoid using 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 bridge.