From $\boldsymbol{\logπ}$ to $\boldsymbolπ$: Taming Divergence in Soft Clipping via Bilateral Decoupled Decay of Probability Gradient Weight

• URL: http://arxiv.org/abs/2603.14389v1
• Date: Sun, 15 Mar 2026 14:00:48 GMT
• Title: From $\boldsymbol{\logπ}$ to $\boldsymbolπ$: Taming Divergence in Soft Clipping via Bilateral Decoupled Decay of Probability Gradient Weight
• Abstract summary: Reinforcement Learning with Verifiable Rewards (RLVR) has catalyzed a leap in Large Language Model (LLM) reasoning, yet its optimization dynamics remain fragile.<n>Standard algorithms like GRPO enforce stability via hard clipping'', which inadvertently stifles exploration by discarding gradients of tokens outside the trust region.<n>We propose Decoupled Gradient Policy Optimization (DGPO), which employs a decoupled decay mechanism based on importance sampling ratios.
• Score: 6.07556923512707
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Reinforcement Learning with Verifiable Rewards (RLVR) has catalyzed a leap in Large Language Model (LLM) reasoning, yet its optimization dynamics remain fragile. Standard algorithms like GRPO enforce stability via ``hard clipping'', which inadvertently stifles exploration by discarding gradients of tokens outside the trust region. While recent ``soft clipping'' methods attempt to recover these gradients, they suffer from a critical challenge: relying on log-probability gradient ($\nabla_θ\log π_θ$) yields divergent weights as probabilities vanish, destabilizing LLM training. We rethink this convention by establishing probability gradient ($\nabla_θπ_θ$) as the superior optimization primitive. Accordingly, we propose Decoupled Gradient Policy Optimization (DGPO), which employs a decoupled decay mechanism based on importance sampling ratios. By applying asymmetric, continuous decay to boundary tokens, DGPO resolves the conflict between stability and sustained exploration. Extensive experiments across DeepSeek-R1-Distill-Qwen series models (1.5B/7B/14B) demonstrate that DGPO consistently outperforms strong baselines on various mathematical benchmarks, offering a robust and scalable solution for RLVR. Our code and implementation are available at: https://github.com/VenomRose-Juri/DGPO-RL.

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