Taming Extreme Tokens: Covariance-Aware GRPO with Gaussian-Kernel Advantage Reweighting
For LLM reasoning training, this method addresses instability in GRPO without hyperparameter tuning.
GRPO struggles with exploration-exploitation tradeoff. The proposed covariance-aware method with Gaussian-kernel reweighting improves reasoning benchmarks and stabilizes entropy during training.
Group Relative Policy Optimization (GRPO) has emerged as a promising approach for improving the reasoning capabilities of large language models. However, it struggles to effectively balance the tradeoff between exploration and exploitation during training, often resulting in suboptimal performance. Motivated by the theoretical insight that changes in entropy are governed by the covariance between token probabilities and their corresponding advantages, we propose a hyperparameter-free, covariance-weighted optimization method that dynamically down-weights extreme token-level updates via a Gaussian kernel. This approach automatically reduces the instability caused by exploration-exploitation trade-off while preserving informative learning signals. Extensive empirical evaluations show that our approach improves downstream performance across reasoning benchmarks compared with GRPO, and effectively stablizes entropy as training progresses.