CPMöbius: Iterative Coach–Player Reasoning for Data-Free Reinforcement Learning

Large Language Models (LLMs) have demonstrated strong potential in complex reasoning, yet their progress remains fundamentally constrained by reliance on massive high-quality human-curated tasks and labels, either through supervised fine-tuning (SFT) or reinforcement learning (RL) on reasoning-specific data. This dependence renders supervision-heavy training paradigms increasingly unsustainable, with signs of diminishing scalability already evident in practice. To overcome this limitation, we introduce CPMöbius, a collaborative Coach–Player paradigm for data-free reinforcement learning of reasoning models. Unlike traditional adversarial self-play frameworks, CPMöbius inspired by multi-agent collaboration treats the Coach and Player as independent but cooperative roles. The Coach proposes instructions targeted at the Player’s capability and receives rewards based on changes in the Player’s performance, while the Player is rewarded for solving the increasingly instructive tasks generated by the Coach. This cooperative optimization loop is designed to directly enhance the Player’s mathematical reasoning ability. Remarkably, CPMöbius achieves substantial improvement without relying on any external training data, outperforming existing unsupervised approaches. For example, on the Qwen2.5-Math-7B-Instruct, our method improves accuracy by overall average +4.9 and out-of-distribution average +5.4, which exceed RENT for +1.5 on overall accuracy and R-zero for +4.2 on OOD accuracy.