Learning to Reason under Off-Policy Guidance

• URL: http://arxiv.org/abs/2504.14945v5
• Date: Sun, 22 Jun 2025 00:18:09 GMT
• Title: Learning to Reason under Off-Policy Guidance
• Authors: Jianhao Yan, Yafu Li, Zican Hu, Zhi Wang, Ganqu Cui, Xiaoye Qu, Yu Cheng, Yue Zhang,
• Abstract summary: We introduce textbfLUFFY (textbfLearning to reason textbfUnder otextbfFF-polictextbfY guidance), a framework that augments textitRLVR with off-policy reasoning traces.<n>LUFFY balances imitation and exploration by combining off-policy demonstrations with on-policy rollouts during training.
• Score: 40.27817638425237
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recent advances in large reasoning models (LRMs) demonstrate that sophisticated behaviors such as multi-step reasoning and self-reflection can emerge via reinforcement learning with verifiable rewards~(\textit{RLVR}). However, existing \textit{RLVR} approaches are inherently ``on-policy'', limiting learning to a model's own outputs and failing to acquire reasoning abilities beyond its initial capabilities. To address this issue, we introduce \textbf{LUFFY} (\textbf{L}earning to reason \textbf{U}nder o\textbf{FF}-polic\textbf{Y} guidance), a framework that augments \textit{RLVR} with off-policy reasoning traces. LUFFY dynamically balances imitation and exploration by combining off-policy demonstrations with on-policy rollouts during training. Specifically, LUFFY combines the Mixed-Policy GRPO framework, which has a theoretically guaranteed convergence rate, alongside policy shaping via regularized importance sampling to avoid superficial and rigid imitation during mixed-policy training. Compared with previous RLVR methods, LUFFY achieves an over \textbf{+6.4} average gain across six math benchmarks and an advantage of over \textbf{+6.2} points in out-of-distribution tasks. Most significantly, we show that LUFFY successfully trains weak models in scenarios where on-policy RLVR completely fails. These results provide compelling evidence that LUFFY transcends the fundamental limitations of on-policy RLVR and demonstrates the great potential of utilizing off-policy guidance in RLVR.

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