# Generalized Proximal Policy Optimization: Unifying LLM RL Algorithms from the Perspective of Divergence

arXiv: https://arxiv.org/abs/2610.13015 · HTML: https://mlsanity.com/paper/2610.13015/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 23 of its 27 references that are in the map.
- First posted on arXiv 9 Oct 2026.

## Placed in

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

## Builds on (most cited first, 23 of 23)

- [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)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [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)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention](https://mlsanity.com/paper/2506.13585/) (2025)
- [Mastering Complex Control in MOBA Games with Deep Reinforcement Learning](https://mlsanity.com/paper/1912.09729/) (2019)
- [Geometric-Mean Policy Optimization](https://mlsanity.com/paper/2507.20673/) (2025)
- [Soft Adaptive Policy Optimization](https://mlsanity.com/paper/2511.20347/) (2025)
- [StepCoder: Improve Code Generation with Reinforcement Learning from Compiler Feedback](https://mlsanity.com/paper/2402.01391/) (2024)
- [DCPO: Dynamic Clipping Policy Optimization](https://mlsanity.com/paper/2509.02333/) (2025)
- [Rethinking the Trust Region in LLM Reinforcement Learning](https://mlsanity.com/paper/2602.04879/) (2026)
- [Beyond Euclidean Clipping: Overcoming Exploration Collapse in LLM RL via Riemannian Isometric Policy Optimization](https://mlsanity.com/paper/2607.10169/) (2026)

## Abstract (arXiv)

Reinforcement learning has become the foundational paradigm for enhancing the reasoning capabilities of LLMs. Yet the dominant approach, Proximal Policy Optimization (PPO), relies on a geometrically degenerate clipping proxy that cannot adapt its resistance to policy shifts, leading to premature clipping and degraded exploration. Subsequent variants alleviate these issues through fragmented and heuristic modifications. We propose Generalized Proximal Policy Optimization (GPPO), a principled and unified framework for understanding and designing LLM RL algorithms through the lens of divergence. We establish a generalized f-divergence trust-region theory with a monotonic performance improvement guarantee, and show that different f-divergences induce distinct geometries and policy update dynamics. We further introduce novel estimator topologies that provide more faithful divergence estimates than the conventional single-sample Monte Carlo estimation. Under this framework, PPO and recent variants such as DAPO, DPPO, and RIPO emerge as special cases, establishing a principled two-dimensional design space of Divergence × Estimator. Extensive experiments on eight competition-level math and coding benchmarks show that both dimensions are critical. The best-performing GPPO instantiation surpasses standard GRPO by up to 50% and 14% on math and coding, delivering SOTA performance.