TREK: Distill to Explore, Reinforce to Refine
2026-07-06 • Machine Learning
Machine LearningArtificial Intelligence
AI summaryⓘ
The authors introduce TREK, a method to help a learning model improve on difficult problems where it previously struggled. Instead of just copying a teacher, TREK uses verified correct answers from a teacher to expand the model's understanding and guide its exploration. This approach allows the model to better learn and solve hard tasks more quickly. The authors show TREK improves performance on math problems and interactive agent tasks, often needing fewer training steps than previous methods.
Group Relative Policy OptimizationTREKpolicy distillationforward KL divergenceexplorationverified trajectoriesmathematical reasoning benchmarksagentic tasksmodel refinement
Authors
Yuanda Xu, Zhengze Zhou, Kayhan Behdin, Jelena Markovic-Voronov, Hejian Sang, Xiaomin Li, Wenhui Zhu, Xinchen Du, Aida Rahmattalabi, Ran He, Sen Na, Zhipeng Wang, Alborz Geramifard
Abstract
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.