A Gradient Perspective on RLVR Stability and Winner Advantage Policy Optimization

2026-06-14

AI Summary

This work addresses the instability commonly observed in group relative policy optimization (GRPO) methods within reinforcement learning for verifiable reasoning (RLVR). By analyzing token-level gradient dynamics, the study uncovers how policy updates influence the probability and entropy of subsequent tokens. Building on this insight, the authors propose Winner Advantage Policy Optimization (WAPO), which restricts policy updates to samples with positive advantage estimates. WAPO further introduces a stability-oriented classification framework that leverages both advantage signs and token distributions, enabling a simple yet effective online gradient clipping objective. Experimental results demonstrate that WAPO substantially enhances training stability and achieves competitive or superior performance over existing baselines on mathematical reasoning and multi-hop question answering tasks, while maintaining compatibility across diverse model architectures.

Abstract

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.

Problem

• Reinforcement Learning with Verifiable Rewards
• Training Stability
• Policy Optimization
• Gradient Dynamics
• Language Model Reasoning

Innovation

• Gradient Dynamics
• Policy Optimization
• Reinforcement Learning with Verifiable Rewards
• Token-level Analysis
• Winner Advantage