SAW: Stage-Aware Dynamic Weighting for Multi-Objective Reinforcement Learning in Large Language Models

Although multi-objective reinforcement learning (MORL) is central to aligning large language models with complex human preferences, the prevailing practice of static weighted summation overlooks a more fundamental phenomenon: reward learning is markedly asynchronous across objectives. Well-learned dimensions quickly produce homogeneous, low-variance signals whose residual noise contaminates the aggregated reward (in GRPO) or occupies a fixed share of the advantage budget (in GDPO), interfering with the scarce yet high-value signals carried by under-learned dimensions. To address this asynchrony, we propose Stage-Aware Dynamic Weighting (SAW), a lightweight, algorithm-agnostic dynamic weighting mechanism. SAW utilizes the coefficient of variation (CV) as a scale-invariant proxy for real-time informativeness, reweighting each dimension's reward or advantage contribution by its relative informativeness within the batch. Unlike gradient-based methods that require multiple forward and backward passes, SAW relies solely on batch-level statistics, introducing nearly negligible computational overhead. Experiments on tool-calling and text summarization tasks demonstrate that SAW consistently improves both training efficiency and final performance under both GRPO and GDPO frameworks, confirming it as a general-purpose plug-in for multi-reward LLM alignment. Our code is available at https://github.com/Zhaolutuan/SAW