用弱模型训练强模型，Qwen3-1.7B在AIME 2024从48.3%飙到62.4%，只花4小时8卡A100。比直接RL还省，值得试试。
RLVR通过可验证奖励提升推理能力，但每次训练强模型需要大量采样，成本高昂。Direct-OPD方案在小模型上执行RL，将其策略偏移作为隐式奖励传递给强模型。对比后RL教师与前RL参考的对数比率，为学生模型提供密集监督。实验显示，Direct-OPD将Qwen3-1.7B在AIME 2024上的准确率从48.3%提升至62.4%，仅需8块A100 GPU训练4小时。该方法优于step-matched直接RL，并支持多策略偏移的级联组合。
Weak-to-Strong Generalization via Direct On-Policy Distillation
Reinforcement learning with verifiable rewards (RLVR) is a powerful recipe for improving language-model reasoning, but it is expensive to repeat on every new strong model because the target model must generate many rollouts during training. As models scale, post-training itself becomes a bottleneck. We study a weak-to-strong alternative: run RL on a smaller model where rollouts are cheaper, then reuse what that RL run learned to improve a stronger target model. Directly distilling the post-RL weak teacher is not enough, because the teacher's final policy mixes useful RL gains with the limitations of the smaller model. We propose Direct On-Policy Distillation (Direct-OPD), which transfers the teacher's RL-induced policy shift instead. Direct-OPD compares the post-RL teacher with its own pre-RL reference and treats their log-ratio as a dense implicit reward for the student. In plain terms, the checkpoint pair tells us which actions RL made the weak model more or less likely to take, and Direct-OPD applies that signal on the stronger student's own on-policy states. This directly reuses the weak model's RL supervision signal without training an explicit reward model or running sparse-reward RL on the target model. Empirically, Direct-OPD consistently leverages weaker teachers to improve stronger target models; notably, it boosts Qwen3-1.7B from 48.3% to 62.4% on AIME 2024 in just 4 hours on 8 A100 GPUs. It outperforms step-matched direct RL and enables the sequential composition of multiple policy shifts. Our results show that RL outcomes can be reused across model scales as implicit reward signals, not merely as final models to imitate.