TREK: Distill to Explore, Reinforce to Refine

Source

• Source name: arXiv
• Source kind: paper
• Authors / organization: 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
• Venue: arXiv: cs.LG
• Published: 2026-07-06
• Collected: 2026-07-07
• URL: http://arxiv.org/abs/2607.05339v1
• PDF: https://arxiv.org/pdf/2607.05339v1
• DOI: UNKNOWN

Plain-Language Brief

The research presents TREK (Teacher-Routed Exploration via Forward KL), a method that uses distillation for exploration support expansion, rather than imitation. This method can be used with various types of teachers and models, and it improves the performance of Qwen3 models on mathematical reasoning tasks like AIME 2024 and AIME 2025. It also increases the success rate of ALFWorld and ScienceWorld tasks for agentic tasks.

What the Document Says

• The paper introduces Group Relative Policy Optimization (GRPO) and TREK (Teacher-Routed Exploration via Forward KL).
• GRPO is effective when the current policy samples useful reasoning trajectories but stalls on hard prompts.
• TREK uses distillation for exploration support expansion, not imitation.
• TREK can use various types of teachers and models, and it can identify which hard-prompt samples are most worth consolidating even when teacher internals are unavailable.
• TREK identifies prompts where the unaided student has a low pass rate, queries a proposal source to produce verified candidate solutions, 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.
• DeepSeek-V4 proposals with TREK improve Qwen3 models on AIME 2024 and AIME 2025 across all tested scales.
• For Qwen3-8B, TREK 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.

Key Concepts Mentioned

• Group Relative Policy Optimization (GRPO)
• Teacher-Routed Exploration via Forward KL (TREK)
• DeepSeek-V4
• Qwen3
• AIME
• ALFWorld
• ScienceWorld

Claims Made by the Document

• TREK improves Qwen3 models on mathematical reasoning tasks.
• TREK increases the success rate of ALFWorld and ScienceWorld tasks for agentic tasks.

Evidence Used

• Improvements in AIME scores and success rates of ALFWorld and ScienceWorld tasks mentioned in the text

Methods / Approach

• Group Relative Policy Optimization (GRPO)
• Teacher-Routed Exploration via Forward KL (TREK)

Limitations Stated by the Authors

Unknown

Limitations Noted by the Agent

Agent interpretation — not from the source.

The paper does not discuss the limitations of TREK or GRPO in this specific text.

Open Questions

• What are the potential limitations of TREK and GRPO?
• How does TREK compare to other exploration support expansion methods?

Notes for Future Q&A

May include interpretation. Labeled where it does.

• The paper does not discuss the limitations of TREK or GRPO in this specific text.
• It is unknown if TREK compares favorably to other exploration support expansion methods.

Raw Abstract / Excerpt

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.