# Train4Merge: A Controlled Single-Teacher Study of RL vs. SFT Teachers for OPD-Based Model Merging

arXiv: https://arxiv.org/abs/2609.32303 · HTML: https://mlsanity.com/paper/2609.32303/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for LLM agents, one of 16 directions in LLM agents and tool use.
- Builds on 29 of its 34 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Placed in

- LLM agents and tool use / [Reinforcement learning for LLM agents](https://mlsanity.com/agents/reinforcement-learning-for-llm-agents/)
- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 29 of 29)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?](https://mlsanity.com/paper/2403.14624/) (2024)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [OS-ATLAS: A Foundation Action Model for Generalist GUI Agents](https://mlsanity.com/paper/2410.23218/) (2024)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [Scaling Computer-Use Grounding via User Interface Decomposition and Synthesis](https://mlsanity.com/paper/2505.13227/) (2025)
- [Vision-OPD: Learning to See Fine Details for Multimodal LLMs via On-Policy Self-Distillation](https://mlsanity.com/paper/2605.18740/) (2026)
- [MobileWorld: Benchmarking Autonomous Mobile Agents in Agent-User Interactive and MCP-Augmented Environments](https://mlsanity.com/paper/2512.19432/) (2025)
- [MMBench-GUI: Hierarchical Multi-Platform Evaluation Framework for GUI Agents](https://mlsanity.com/paper/2507.19478/) (2025)
- [TCOD: Exploring Temporal Curriculum in On-Policy Distillation for Multi-turn Autonomous Agents](https://mlsanity.com/paper/2604.24005/) (2026)
- [Long-Horizon-Terminal-Bench: Testing the Limits of Agents on Long-Horizon Terminal Tasks with Dense Reward-Based Grading](https://mlsanity.com/paper/2607.08964/) (2026)
- [Rethinking On-Policy Distillation of Large Language Models II: One Training Example](https://mlsanity.com/paper/2609.04172/) (2026)
- [On Predictability of Reinforcement Learning Dynamics for Large Language Models](https://mlsanity.com/paper/2510.00553/) (2025)
- [Learning to Foresee: Unveiling the Unlocking Efficiency of On-Policy Distillation](https://mlsanity.com/paper/2605.11739/) (2026)
- [Mitigating Forgetting Between Supervised and Reinforcement Learning Yields Stronger Reasoners](https://mlsanity.com/paper/2510.04454/) (2025)
- [On-policy Distillation with Verifiable Reward](https://mlsanity.com/paper/2608.24696/) (2026)
- [Learn where to Click from Yourself: On-Policy Self-Distillation for GUI Grounding](https://mlsanity.com/paper/2605.00642/) (2026)
- [UI-MOPD: Multi-Platform On-Policy Distillation for Unified GUI Agents](https://mlsanity.com/paper/2607.04425/) (2026)
- [Less is Enough: Synthesizing Diverse Data in LLM Feature Space with Sparse Autoencoders](https://mlsanity.com/paper/2602.10388/) (2026)
- [Trust the Right Teacher: Quality-Aware Self-Distillation for GUI Grounding](https://mlsanity.com/paper/2606.18101/) (2026)
- [The Physics of Multi-Turn Long-Horizon Planning: From Pre-training to Post-training via Single- and Multi-Teacher On-Policy Agentic Distillation](https://mlsanity.com/paper/2607.24720/) (2026)
- [MAGA: Multi-Platform Self-Fusion of GUI Agents via Structured Action Distillation](https://mlsanity.com/paper/2607.29320/) (2026)
- [Enough is as good as a feast: A Comprehensive Analysis of How Reinforcement Learning Mitigates Task Conflicts in LLMs](https://mlsanity.com/paper/2607.22039/) (2026)

## Abstract (arXiv)

Domain experts trained from a shared checkpoint can transfer their specialized capabilities to a single student through on-policy distillation (OPD). Existing research primarily focuses on improving this merging process, while the algorithms used to train the experts have received limited systematic comparison. We investigate which training algorithm produces teachers better suited to OPD through controlled single-teacher comparisons of supervised fine-tuning (SFT) and reinforcement learning (RL) across Agentic, Reasoning, and Perception. Teachers and students share the same Qwen3.5-9B initialization, and the two teacher types are compared at similar task performance. Our experiments show that RL teachers yield stronger students and higher recovery of teacher performance gains across all three domains. At their best checkpoints, RL-guided students outperform SFT-guided students by 4.27, 1.50, and 0.86 percentage points, respectively. In Agentic, the best SFT-guided student recovers only 44.44% of its teacher's performance gain over the base model, whereas the best RL-guided student recovers 115.00%, surpassing its teacher. Our further analysis shows that RL teachers undergo smaller parameter displacements from the shared initialization than SFT teachers. These findings support the hypothesis that RL teachers' smaller departures from the student's starting point facilitate learning through OPD, resulting in stronger students.