Scaling Behaviors of LLM Reinforcement Learning Post-Training: An Empirical Study in Mathematical Reasoning
作者: Zelin Tan, Hejia Geng, Xiaohang Yu, Mulei Zhang, Guancheng Wan, Yifan Zhou, Qiang He, Xiangyuan Xue, Heng Zhou, YuTao Fan, Zhong-Zhi Li, Zaibin Zhang, Guibin Zhang, Chen Zhang, Zhenfei Yin, Philip Torr, Lei Bai
摘要
While scaling laws for large language models (LLMs) during pre-training have been extensively studied, their behavior under reinforcement learning (RL) post-training remains largely unexplored. This paper investigates the scaling behavior of Large Language Model (LLM) reinforcement learning post-training, focusing on mathematical reasoning. Through experiments across the Qwen2.5 series (0.5B to 72B), we characterize how model scale, data, and compute interact. Our analysis yields four key findings: 1. Larger models consistently demonstrate superior compute and data efficiency. 2. The relationship between model performance and training resources follows a predictive power-law across both base and instruction-tuned models. 3. RL learning efficiency exhibits a latent saturation trend with increasing model scale. 4. In data-constrained regimes, performance is primarily driven by the total volume of training data rather than sample uniqueness. These results offer practical guidelines for scaling reasoning capabilities through reinforcement learning post-training.