How to Allocate, How to Learn? Dynamic Rollout Allocation and Advantage Modulation for Policy Optimization

Reinforcement learning with verifiable rewards (RLVR) has emerged as a highly effective framework for improving LLM reasoning, with methods such as GRPO among its most successful instantiations. However, GRPO relies on repeated generation of long chain-of-thought rollouts. Training time scales with the number of rollouts, a large fraction of which are uninformative. Thus, GRPO is computationally expensive and unstable. To mitigate this, existing approaches either generate a larger pool of rollouts and filter the most informative prompts, or leverage historical signals for filtering at later stages of training. These strategies offer modest performance gains, but slow down the overall process. To address this, we propose VarIance Guided Online Rollout allocation (VIGOR) which instead of allocating a fixed rollout budget per example, begins with a small number of rollouts for all examples in a batch and iteratively allocates additional rollouts to those with the highest group reward variance until a fixed total rollout budget is reached. Theoretically, we show that under RLVR, reward variance controls the gradient magnitude, and derive VIGOR's closed-form speedup ratio over GRPO, which grows with refinement rounds under Pareto-distributed reward variance. Experiments on mathematical reasoning and coding tasks show that VIGOR reaches target accuracy with up to 2.3$\times$ fewer rollouts on math, reaches GRPO's final coding full pass rate with 1.49$\times$ fewer rollouts, and improves the coding average test pass rate by 3.4 points.

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.