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 \textit{Disproportionate Weight Divergence (DWD)} phenomenon: performance degradation is synchronized with a sharp surge in the \texttt{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 \texttt{lm_head} while intermediate layers are structurally attenuated, and (ii) the \texttt{lm_head} gradient norm lower-bounds the policy divergence. These results establish the \texttt{lm_head} gradient norm as a principled, real-time signal of catastrophic policy shift. Guided by this insight, we propose \textit{Dynamic Gradient Gating (DGG)}, a lightweight intervention that monitors the \texttt{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× sample efficiency and 2.14× wall-clock speedup across math, ALFWorld, WebShop, and search-augmented QA tasks.
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× fewer rollouts on math, reaches GRPO's final coding full pass rate with 1.49× fewer rollouts, and improves the coding average test pass rate by 3.4 points.
Reinforcement Learning with Verifiable Rewards (RLVR) trains reasoning models without labeled trajectories, relying on grouped rollouts to expose the policy to alternative reasoning paths and a verifier to score them. Rollout diversity has accordingly emerged as a central bottleneck in RLVR, with most existing methods broadening exploration through temperature, prefix, or rollout-selection adjustments. We identify a structurally distinguished but overlooked position for broadening this diversity: the first token after the reasoning marker. The policy's first-token distribution exhibits a sharply peaked yet correctness-decoupled phenomenon, and this first token position can broaden the regions a rollout group covers without altering the correctness signal. We introduce REFT (Rollout Exploration with First-Token Diversification), a light addition to the RLVR pipeline that samples first tokens uniformly from the policy's own top-N candidates and allocates rollouts evenly, leaving every other component unchanged. Trained on the resulting diversified rollouts, REFT improves aggregate Pass@1, Pass@8, and Pass@64 over DAPO and GRPO baselines across four base models (0.5B-7B) and three difficulty regimes.
Reinforcement learning with verifiable rewards (RLVR) improves language-model reasoning, but GRPO-style optimization remains prone to collapse. We analyse this instability through token-level gradient dynamics, deriving a taxonomy that predicts how updates affect next-token probabilities and entropy. The taxonomy shows that stability depends jointly on the advantage sign and token distribution under the current policy. Motivated by this finding, we propose Winner Advantage Policy Optimization (WAPO), a simple online clipped policy-gradient objective that updates only on positive-advantage completions. Across mathematical reasoning and multi-hop QA benchmarks, WAPO improves training stability and matches or outperforms baselines across multiple model families. Full code can be found at https://github.com/layer6ai-labs/wapo.