# DCPO: Dynamic Clipping Policy Optimization

arXiv: https://arxiv.org/abs/2509.02333 · HTML: https://mlsanity.com/paper/2509.02333/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 16 of its 18 references that are in the map.
- First posted on arXiv 2 Sep 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 16 of 16)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks](https://mlsanity.com/paper/2504.05118/) (2025)
- [Mastering Complex Control in MOBA Games with Deep Reinforcement Learning](https://mlsanity.com/paper/1912.09729/) (2019)

## Built on by (most cited first, 30 of 40)

- [Rethinking Entropy Interventions in RLVR: An Entropy Change Perspective](https://mlsanity.com/paper/2510.10150/) (2025)
- [BAPO: Stabilizing Off-Policy Reinforcement Learning for LLMs via Balanced Policy Optimization with Adaptive Clipping](https://mlsanity.com/paper/2510.18927/) (2025)
- [Single-Rollout Asynchronous Optimization for Agentic Reinforcement Learning](https://mlsanity.com/paper/2607.07508/) (2026)
- [VOLD: Reasoning Transfer from LLMs to Vision-Language Models via On-Policy Distillation](https://mlsanity.com/paper/2510.23497/) (2025)
- [SRPO: Self-Referential Policy Optimization for Vision-Language-Action Models](https://mlsanity.com/paper/2511.15605/) (2025)
- [When Importance Sampling Misallocates Credit: Asymmetric Ratios for Outcome-Supervised RL](https://mlsanity.com/paper/2510.06062/) (2025)
- [Heterogeneous Agent Collaborative Reinforcement Learning](https://mlsanity.com/paper/2603.02604/) (2026)
- [Baichuan-M3: Modeling Clinical Inquiry for Reliable Medical Decision-Making](https://mlsanity.com/paper/2602.06570/) (2026)
- [Contextual Rollout Bandits for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2602.08499/) (2026)
- [MASPO: Unifying Gradient Utilization, Probability Mass, and Signal Reliability for Robust and Sample-Efficient LLM Reasoning](https://mlsanity.com/paper/2602.17550/) (2026)
- [ESPO: Entropy Importance Sampling Policy Optimization](https://mlsanity.com/paper/2512.00499/) (2025)
- [Explore Data Left Behind in Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2511.04800/) (2025)
- [A Step Back: Prefix Importance Ratio Stabilizes Policy Optimization](https://mlsanity.com/paper/2601.22718/) (2026)
- [LaDi-RL: Latent Diffusion Reasoning Prevents Entropy Collapse in Reinforcement Learning](https://mlsanity.com/paper/2602.01705/) (2026)
- [Revisiting DAgger in the Era of LLM-Agents](https://mlsanity.com/paper/2605.12913/) (2026)
- [Advantage Collapse in Group Relative Policy Optimization: Diagnosis and Mitigation](https://mlsanity.com/paper/2605.21125/) (2026)
- [Stabilizing Policy Gradients for Sample-Efficient Reinforcement Learning in LLM Reasoning](https://mlsanity.com/paper/2510.00819/) (2025)
- [Can GRPO Help LLMs Transcend Their Pretraining Origin?](https://mlsanity.com/paper/2510.15990/) (2025)
- [SSPO: Subsentence-level Policy Optimization](https://mlsanity.com/paper/2511.04256/) (2025)
- [ReLaX: Reasoning with Latent Exploration for Large Reasoning Models](https://mlsanity.com/paper/2512.07558/) (2025)
- [Pinpointing crucial steps: Attribution-based Credit Assignment for Verifiable Reinforcement Learning](https://mlsanity.com/paper/2510.08899/) (2025)
- [QUATRO: Query-Adaptive Trust Region Policy Optimization for LLM Fine-tuning](https://mlsanity.com/paper/2602.04620/) (2026)
- [Beyond Euclidean Clipping: Overcoming Exploration Collapse in LLM RL via Riemannian Isometric Policy Optimization](https://mlsanity.com/paper/2607.10169/) (2026)
- [Back to Basics: Revisiting Exploration in Reinforcement Learning for LLM Reasoning via Generative Probabilities](https://mlsanity.com/paper/2602.05281/) (2026)
- [Chart Specification: Structural Representations for Incentivizing VLM Reasoning in Chart-to-Code Generation](https://mlsanity.com/paper/2602.10880/) (2026)
- [Policy Improvement Reinforcement Learning](https://mlsanity.com/paper/2604.00860/) (2026)
- [Online Causal Kalman Filtering for Stable and Effective Policy Optimization](https://mlsanity.com/paper/2602.10609/) (2026)
- [Stabilizing Policy Optimization via Logits Convexity](https://mlsanity.com/paper/2603.00963/) (2026)
- [Skip-Connected Policy Optimization for Implicit Advantage](https://mlsanity.com/paper/2604.08690/) (2026)
- [MCPO: Mastery-Consolidated Policy Optimization for Large Reasoning Models](https://mlsanity.com/paper/2604.16972/) (2026)

## Abstract (arXiv)

Reinforcement Learning from Verifiable Rewards (RLVR) has emerged as a promising framework for enhancing the reasoning capabilities of large language models. However, existing approaches such as GRPO often suffer from zero gradients. This problem arises primarily due to fixed clipping bounds for token-level probability ratios and the standardization of identical rewards, which can lead to ineffective gradient updates and underutilization of generated responses. In this work, we propose Dynamic Clipping Policy Optimization(DCPO), which introduces a dynamic clipping strategy that adaptively adjusts clipping bounds based on token-specific prior probabilities to enhance token-level exploration, and a smooth advantage standardization technique that standardizes rewards across cumulative training steps to improve the response-level effective utilization of generated responses. DCPO achieved state-of-the-art performance on four benchmarks based on four different models. In particular, DCPO achieved an Avg@1 of 46.7 under greedy decoding and an Avg@32 of 38.8 under 32 times sampling on the AIME24 benchmark, surpassing DAPO (36.7/31.6), GRPO (36.7/32.1) and GSPO (40.0/34.9) on the Qwen2.5-Math-7B model. On the AIME25 benchmark based on Qwen2.5-14B, DCPO achieves a performance of (23.3/19.0), surpassing GRPO (13.3/10.5), DAPO (20.0/15.3) and GSPO (16.7/9.9). Furthermore, DCPO achieved an average 28% improvement in the nonzero advantage over GRPO in four models, doubled the training efficiency over DAPO, and significantly reduced the token clipping ratio by an order of magnitude compared to both GRPO and DAPO, while achieving superior performance. These results highlight DCPO's effectiveness in leveraging generated data more efficiently for reinforcement learning in large language models.