# Comparative Analysis and Parametric Tuning of PPO, GRPO, and DAPO for LLM Reasoning Enhancement

arXiv: https://arxiv.org/abs/2512.07611 · HTML: https://mlsanity.com/paper/2512.07611/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 18 of its 29 references that are in the map.
- First posted on arXiv 8 Dec 2025.

## Placed in

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

## Builds on (most cited first, 18 of 18)

- [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)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [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)
- [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)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [REINFORCE++: Stabilizing Critic-Free Policy Optimization with Global Advantage Normalization](https://mlsanity.com/paper/2501.03262/) (2025)
- [It Takes Two: Your GRPO Is Secretly DPO](https://mlsanity.com/paper/2510.00977/) (2025)
- [GTPO and GRPO-S: Token and Sequence-Level Reward Shaping with Policy Entropy](https://mlsanity.com/paper/2508.04349/) (2025)
- [A Closer Look at Deep Policy Gradients](https://mlsanity.com/paper/1811.02553/) (2018)
- [SCOPE-RL: Stable and Quantitative Control of Policy Entropy in RL Post-Training](https://mlsanity.com/paper/2510.08141/) (2025)
- [MobileLLM-R1: Exploring the Limits of Sub-Billion Language Model Reasoners with Open Training Recipes](https://mlsanity.com/paper/2509.24945/) (2025)

## Built on by (most cited first, 2 of 2)

- [MMR-GRPO: Accelerating GRPO-Style Training through Diversity-Aware Reward Reweighting](https://mlsanity.com/paper/2601.09085/) (2026)
- [ReCrit: Transition-Aware Reinforcement Learning for Scientific Critic Reasoning](https://mlsanity.com/paper/2605.18799/) (2026)

## Abstract (arXiv)

This study presents a systematic comparison of three Reinforcement Learning (RL) algorithms (PPO, GRPO, and DAPO) for improving complex reasoning in large language models (LLMs). Our main contribution is a controlled transfer-learning evaluation: models are first fine-tuned on the specialized Countdown Game and then assessed on a suite of general-purpose reasoning benchmarks. Across all tasks, RL-trained models outperform their corresponding base models, although the degree of improvement differs by benchmark. Our parametric analysis offers practical guidance for RL-based LLM training. Increasing the group size in GRPO and DAPO leads to more stable training dynamics and higher accuracy, while the impact of the KL-penalty coefficient is non-monotonic. Additionally, we find that the Dynamic Sampling (DS) component in DAPO does not improve performance; in fact, the best overall results are achieved with DAPO when DS is disabled.