ΔL Normalization: Rethink Loss Aggregation in RLVR
Authors: name: Zhiyuan He, name: Xufang Luo, name: Yike Zhang, name: Yuqing Yang, name: Lili Qiu

We propose Delta L 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 Delta L Normalization 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. Our code will
be made public at https://github.com/zerolllin/Delta-L-Normalization.