# Trust Region Preference Approximation: A simple and stable reinforcement learning algorithm for LLM reasoning

arXiv: https://arxiv.org/abs/2504.04524 · HTML: https://mlsanity.com/paper/2504.04524/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 25 of its 49 references that are in the map.
- First posted on arXiv 6 Apr 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)

## Builds on (most cited first, 25 of 25)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Prioritized Experience Replay](https://mlsanity.com/paper/1511.05952/) (2015)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [The Effects of Reward Misspecification: Mapping and Mitigating Misaligned Models](https://mlsanity.com/paper/2201.03544/) (2022)
- [Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models](https://mlsanity.com/paper/2410.07985/) (2024)
- [Human-level performance in first-person multiplayer games with population-based deep reinforcement learning](https://mlsanity.com/paper/1807.01281/) (2018)
- [KTO: Model Alignment as Prospect Theoretic Optimization](https://mlsanity.com/paper/2402.01306/) (2024)
- [Logic-RL: Unleashing LLM Reasoning with Rule-Based Reinforcement Learning](https://mlsanity.com/paper/2502.14768/) (2025)
- [Direct Language Model Alignment from Online AI Feedback](https://mlsanity.com/paper/2402.04792/) (2024)
- [Smaug: Fixing Failure Modes of Preference Optimisation with DPO-Positive](https://mlsanity.com/paper/2402.13228/) (2024)
- [Imitate, Explore, and Self-Improve: A Reproduction Report on Slow-thinking Reasoning Systems](https://mlsanity.com/paper/2412.09413/) (2024)
- [Token-level Direct Preference Optimization](https://mlsanity.com/paper/2404.11999/) (2024)
- [On Memorization of Large Language Models in Logical Reasoning](https://mlsanity.com/paper/2410.23123/) (2024)
- [Rule Based Rewards for Language Model Safety](https://mlsanity.com/paper/2411.01111/) (2024)
- [Suphx: Mastering Mahjong with Deep Reinforcement Learning](https://mlsanity.com/paper/2003.13590/) (2020)
- [WPO: Enhancing RLHF with Weighted Preference Optimization](https://mlsanity.com/paper/2406.11827/) (2024)
- [Right Now, Wrong Then: Non-Stationary Direct Preference Optimization under Preference Drift](https://mlsanity.com/paper/2407.18676/) (2024)
- [Reveal the Mystery of DPO: The Connection between DPO and RL Algorithms](https://mlsanity.com/paper/2502.03095/) (2025)
- [Minor DPO reject penalty to increase training robustness](https://mlsanity.com/paper/2408.09834/) (2024)

## Built on by (most cited first, 12 of 12)

- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [No Free Lunch: Rethinking Internal Feedback for LLM Reasoning](https://mlsanity.com/paper/2506.17219/) (2025)
- [CME-CAD: Heterogeneous Collaborative Multi-Expert Reinforcement Learning for CAD Code Generation](https://mlsanity.com/paper/2512.23333/) (2025)
- [DisCO: Reinforcing Large Reasoning Models with Discriminative Constrained Optimization](https://mlsanity.com/paper/2505.12366/) (2025)
- [DRPO: Efficient Reasoning via Decoupled Reward Policy Optimization](https://mlsanity.com/paper/2510.04474/) (2025)
- [MEML-GRPO: Heterogeneous Multi-Expert Mutual Learning for RLVR Advancement](https://mlsanity.com/paper/2508.09670/) (2025)
- [Curriculum Reinforcement Learning Can Incentivize Reasoning Capacity in LLMs Beyond the Base Model](https://mlsanity.com/paper/2606.22317/) (2026)
- [Rewards as Labels: Revisiting RLVR from a Classification Perspective](https://mlsanity.com/paper/2602.05630/) (2026)
- [DGRO: Enhancing LLM Reasoning via Exploration-Exploitation Control and Reward Variance Management](https://mlsanity.com/paper/2505.12951/) (2025)
- [ReNCE: Learning to Reason by Noise Contrastive Estimation](https://mlsanity.com/paper/2601.22432/) (2026)
- [Revisiting Reinforcement Learning with Verifiable Rewards from a Contrastive Perspective](https://mlsanity.com/paper/2605.12969/) (2026)

## Abstract (arXiv)

Recently, Large Language Models (LLMs) have rapidly evolved, approaching Artificial General Intelligence (AGI) while benefiting from large-scale reinforcement learning to enhance Human Alignment (HA) and Reasoning. Recent reward-based optimization algorithms, such as Proximal Policy Optimization (PPO) and Group Relative Policy Optimization (GRPO) have achieved significant performance on reasoning tasks, whereas preference-based optimization algorithms such as Direct Preference Optimization (DPO) significantly improve the performance of LLMs on human alignment. However, despite the strong performance of reward-based optimization methods in alignment tasks , they remain vulnerable to reward hacking. Furthermore, preference-based algorithms (such as Online DPO) haven't yet matched the performance of reward-based optimization algorithms (like PPO) on reasoning tasks, making their exploration in this specific area still a worthwhile pursuit. Motivated by these challenges, we propose the Trust Region Preference Approximation (TRPA) algorithm, which integrates rule-based optimization with preference-based optimization for reasoning tasks. As a preference-based algorithm, TRPA naturally eliminates the reward hacking issue. TRPA constructs preference levels using predefined rules, forms corresponding preference pairs, and leverages a novel optimization algorithm for RL training with a theoretical monotonic improvement guarantee. Experimental results demonstrate that TRPA not only achieves competitive performance on reasoning tasks but also exhibits robust stability. The code of this paper are released and updating on https://github.com/XueruiSu/Trust-Region-Preference-Approximation.git.