Scaling up Multi-Turn Off-Policy RL and Multi-Agent Tree Search for LLM Step-Provers

The integration of Large Language Models (LLMs) with automated theorem proving has shown immense promise, yet is constrained by challenges in scaling up both training-time reinforcement learning (RL) and inference-time compute. This paper introduces BFS-Prover-V2, a step-level theorem proving system designed to address this dual scaling problem. We present two primary innovations. The first is a novel multi-turn off-policy RL framework for continually improving the performance of the LLM step-prover at training time. This framework, inspired by the principles of AlphaZero, utilizes a multi-stage expert iteration pipeline featuring adaptive tactic-level data filtering and periodic retraining to surmount the performance plateaus that typically curtail long-term RL in LLM-based agents. The second innovation is a planner-enhanced multi-agent system that scales reasoning capabilities at inference time. This architecture employs a general reasoning model as a high-level planner to iteratively decompose complex theorems into a sequence of simpler subgoals. This hierarchical approach substantially reduces the search space, enabling a team of parallel prover agents to collaborate efficiently by leveraging a shared proof cache. We demonstrate that this dual approach to scaling yields SoTA results on established formal mathematics benchmarks. BFS-Prover-V2 achieves 95.08% and 41.4% on the miniF2F and ProofNet test sets respectively.