VL Norm: Rethink Loss Aggregation in RLVR

Zhiyuan He, Xufang Luo, Yike Zhang, Yuqing Yang, Lili Qiu

Keywords: Reinforcement Learning for LLMs, RLVR, gradient variance reduction

Abstract: We propose VL Norm (Variance-reduced Length-dependent Normalization), a simple yet effective loss aggregation method tailored to the characteristic of dynamic generation lengths in Reinforcement Learning with Verifiable Rewards (RLVR). Recently, RLVR has demonstrated strong potential in improving the reasoning capabilities of large language models (LLMs), but a major challenge lies in the large variability of response lengths during training, which leads to high gradient variance and unstable optimization. Although previous methods such as GRPO, DAPO, and Dr. GRPO introduce different loss normalization terms to address this issue, they either produce biased estimates or still suffer from high gradient variance. By analyzing the effect of varying lengths on policy loss both theoretically and empirically, we reformulate the problem as finding a minimum-variance unbiased estimator. Our proposed VL Norm not only provides an unbiased estimate of the true policy loss but also minimizes gradient variance in theory. Extensive experiments show that it consistently achieves superior results across different model sizes, maximum lengths, and tasks.

Primary Area: foundation or frontier models, including LLMs

Submission Number: 10262