这篇论文给出了一个实用技巧：用蒸馏扩展支持域再强化学习，在数学和代理任务上都涨点明显，而且不需要改动模型结构。
TREK提出一种分阶段训练方法，解决GRPO在困难提示上的探索停滞问题。该方法先用蒸馏将教师模型（如DeepSeek-V4）的已验证轨迹拉入学生模型支持域，再返回标准GRPO精炼。在数学推理中，TREK将Qwen3-8B在AIME 2025上从36.9提升至40.3，在AIME 2024上从47.9提升至51.1（avg@16）。在代理任务上，ALFWorld成功率从75.8提高到82.8，ScienceWorld从12.5提高到26.7。TREK的泛化优势在于仅需已验证输出轨迹，可兼容黑盒或白盒教师。
TREK: Distill to Explore, Reinforce to Refine
Group Relative Policy Optimization (GRPO) is effective when the current policy already samples useful reasoning trajectories, but it stalls on hard prompts whose correct solution modes lie outside the student's on-policy support. We propose TREK (Teacher-Routed Exploration via Forward KL), a simple staged procedure that uses distillation not for imitation but for exploration support expansion. A key advantage of TREK is its generality: because it only consumes verified output trajectories, it can use an external black-box teacher, a white-box teacher, or the same model given additional inference-time context, and it can efficiently identify which hard-prompt samples are most worth consolidating even when teacher internals are unavailable. TREK first identifies prompts where the unaided student has very low pass rate, queries a proposal source to produce verified candidate solutions, keeps the top-$r$ proposals ranked by current student likelihood, applies a short forward-KL phase to pull those verified modes into the student's support, and then returns to standard on-policy GRPO refinement. On mathematical reasoning, TREK with DeepSeek-V4 proposals improves Qwen3 models across all tested scales on AIME 2024 and AIME 2025; for Qwen3-8B, it improves AIME 2025 from 36.9 to 40.3 and AIME 2024 from 47.9 to 51.1 (avg@16), while the self-context variant reaches 38.5 and 49.6 without an external teacher. On agentic tasks, TREK raises ALFWorld success rate from 75.8 to 82.8 and ScienceWorld success rate from 12.5 to 26.7; notably, on the hardest task types, TREK achieves high success rates early in training while unaided GRPO requires substantially more optimization steps to reach comparable levels.