A Gradient Perspective on RLVR Stability and Winner Advantage Policy Optimization
For practitioners training reasoning language models with RLVR, this work provides a simple fix for training collapse, though it is an incremental improvement over existing methods.
RLVR training for language models often collapses; the paper analyzes gradient dynamics and proposes WAPO, which updates only on positive-advantage completions, improving stability and matching or outperforming baselines on math reasoning and multi-hop QA.
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.