From $\log π$ to $π$: Taming Divergence in Soft Clipping via Bilateral Decoupled Decay of Probability Gradient Weight

Reinforcement Learning with Verifiable Rewards (RLVR) has become the dominant paradigm for advanced reasoning in Large Language Models (LLMs), but rollout samples are expensive to obtain, making sample efficiency a critical bottleneck. A natural remedy is to reuse each rollout batch for multiple gradient updates, a standard practice in classical RL. Yet in RLVR, this amplifies policy shift, leading to severe performance degradation. Detecting the onset of degradation early enough to stop reuse remains an open and challenging problem. We close this gap by identifying the Disproportionate Weight Divergence (DWD) phenomenon: performance degradation is synchronized with a sharp surge in the lm\_head weight change, while intermediate layers remain stable. Empirically, we verify that DWD emerges consistently across diverse LLMs and tasks. Theoretically, we prove that (i) harmful gradients concentrate at the lm\_head while intermediate layers are structurally attenuated, and (ii) the lm\_head gradient norm lower-bounds the policy divergence. These results establish the lm\_head gradient norm as a principled, real-time signal of catastrophic policy shift. Guided by this insight, we propose Dynamic Gradient Gating (DGG), a lightweight intervention that monitors the lm\_head gradient norm in real time and intercepts harmful gradients before they corrupt the optimizer. DGG consistently matches or exceeds the standard single-use baseline, achieving up to $2.93\times$ sample efficiency and $2.14\times$ wall-clock speedup across math, ALFWorld, WebShop, and search-augmented QA tasks.

Existing Reinforcement Learning with Verifiable Rewards (RLVR) algorithms, such as GRPO, rely on rigid, uniform, and symmetric trust region mechanisms that are fundamentally misaligned with the complex optimization dynamics of Large Language Models (LLMs). In this paper, we identify three critical challenges in these methods: (1) inefficient gradient utilization caused by the binary cutoff of hard clipping, (2) insensitive probability mass arising from uniform ratio constraints that ignore the token distribution, and (3) asymmetric signal reliability stemming from the disparate credit assignment ambiguity between positive and negative samples. To bridge these gaps, we propose Mass-Adaptive Soft Policy Optimization (MASPO), a unified framework designed to harmonize these three dimensions. MASPO integrates a differentiable soft Gaussian gating to maximize gradient utility, a mass-adaptive limiter to balance exploration across the probability spectrum, and an asymmetric risk controller to align update magnitudes with signal confidence. Extensive evaluations demonstrate that MASPO serves as a robust, all-in-one RLVR solution, significantly outperforming baselines. Our code is available at: https://github.com/FlyTune/MASPO-RL.

Reinforcement learning (RL) has become a key component of post-training large language models (LLMs). In practice, LLM RL is often off-policy because of training-inference mismatch and policy staleness, making trust-region control essential for stable optimization. Mainstream methods such as PPO and GRPO approximate this control with a ratio-clipping mechanism, but the importance ratio can be a poor proxy for distributional shift in long-tailed vocabularies. Recent work such as DPPO addresses this mismatch by replacing ratio-based clipping with a divergence-based mask, yielding a trust region defined by the sampled token's absolute probability shift. However, DPPO still relies on a hard mask: once a token crosses the trust-region boundary in a harmful direction, its gradient is discarded rather than corrected. To address this, we propose Divergence Regularized Policy Optimization (DRPO), which replaces the hard mask with a smooth advantage-weighted quadratic regularizer on policy shift. DRPO preserves the same trust-region geometry as DPPO while inducing bounded, continuous gradient weights that attenuate diverging updates and provide corrective signals beyond the boundary. Experiments across model scales, architectures, and precision settings show that DRPO improves the stability and efficiency of LLM RL training.