SCOPE-RL: Stable and Quantitative Control of Policy Entropy in RL Post-Training

Reinforcement learning (RL) is a key paradigm for post-training large language models (LLMs), but the widely used Group Relative Policy Optimization (GRPO) often suffers from entropy collapse: exploration quickly disappears, policies converge prematurely, and sample diversity declines, ultimately harming training effectiveness. Existing remedies, including entropy bonuses and clip-based methods, rarely keep entropy within a stable exploration regime and often introduce oscillatory entropy or reward degradation. In this work, we identify a previously overlooked asymmetry in entropy dynamics: under high-temperature sampling, positive and negative samples have opposite effects on policy entropy. Specifically, high-temperature positive samples promote entropy growth, whereas negative samples suppress it. We provide a theoretical explanation for this phenomenon: when entropy decreases during policy updates, its derivative with respect to temperature is strictly positive under positive-sample updates, indicating that high-temperature positive samples can counteract entropy decay, thereby slowing entropy collapse and potentially reversing it. Motivated by this insight, we propose SCOPE-RL, a stable and quantitative entropy control framework through a regularization term constructed from temperature-adaptive positive samples. Extensive experiments show that SCOPE-RL consistently outperforms strong RL baselines on both Pass@1 and Pass@$k$. Our results provide evidence that escaping entropy collapse can improve reasoning performance, while also showing that the benefit is non-monotonic, with an optimal level of exploration for RL post-training in reasoning LLMs.