Scaling up Multi-Turn Off-Policy RL and Multi-Agent Tree Search for LLM
  Step-Provers
Authors: name: Ran Xin, name: Zeyu Zheng, name: Yanchen Nie, name: Kun Yuan, name: Xia Xiao

The integration of Large Language Models (LLMs) into automated theorem
proving has shown immense promise, yet is fundamentally constrained by
challenges in scaling up both training-time reinforcement learning (RL) and
inference-time compute. This paper introduces BFS-Prover-V2, a 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 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 search architecture 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 state-of-the-art results on established formal mathematics
benchmarks. BFS-Prover-V2 achieves 95.08\% and 41.4\% on the MiniF2F
and ProofNet test sets respectively. While demonstrated in the domain of formal
mathematics, the RL and inference techniques presented in this work are of
broader interest and may be applied to other domains requiring long-horizon
multi-turn reasoning and complex search.