# Understanding Reinforcement Learning for Model Training, and future directions with GRAPE

arXiv: https://arxiv.org/abs/2509.04501 · HTML: https://mlsanity.com/paper/2509.04501/

## 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 38 of its 73 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/)
- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)
- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 30 of 38)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [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)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [LaMDA: Language Models for Dialog Applications](https://mlsanity.com/paper/2201.08239/) (2022)
- [A General Language Assistant as a Laboratory for Alignment](https://mlsanity.com/paper/2112.00861/) (2021)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [RLAIF vs. RLHF: Scaling Reinforcement Learning from Human Feedback with AI Feedback](https://mlsanity.com/paper/2309.00267/) (2023)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [Curriculum Learning for Reinforcement Learning Domains: A Framework and Survey](https://mlsanity.com/paper/2003.04960/) (2020)
- [Deliberative Alignment: Reasoning Enables Safer Language Models](https://mlsanity.com/paper/2412.16339/) (2024)
- [Debating with More Persuasive LLMs Leads to More Truthful Answers](https://mlsanity.com/paper/2402.06782/) (2024)
- [Curriculum Learning: A Survey](https://mlsanity.com/paper/2101.10382/) (2021)
- [Self-Play Preference Optimization for Language Model Alignment](https://mlsanity.com/paper/2405.00675/) (2024)
- [Large Language Models are Superpositions of All Characters: Attaining Arbitrary Role-play via Self-Alignment](https://mlsanity.com/paper/2401.12474/) (2024)
- [Curriculum Reinforcement Learning from Easy to Hard Tasks Improves LLM Reasoning](https://mlsanity.com/paper/2506.06632/) (2025)
- [Tapered Off-Policy REINFORCE: Stable and efficient reinforcement learning for LLMs](https://mlsanity.com/paper/2503.14286/) (2025)
- [Offline Reinforcement Learning for LLM Multi-Step Reasoning](https://mlsanity.com/paper/2412.16145/) (2024)
- [Self-Alignment of Large Language Models via Monopolylogue-based Social Scene Simulation](https://mlsanity.com/paper/2402.05699/) (2024)
- [Inverse Constitutional AI: Compressing Preferences into Principles](https://mlsanity.com/paper/2406.06560/) (2024)
- [A Critical Evaluation of AI Feedback for Aligning Large Language Models](https://mlsanity.com/paper/2402.12366/) (2024)

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

- [GIM: Evaluating models via tasks that integrate multiple cognitive domains](https://mlsanity.com/paper/2605.18663/) (2026)
- [Training-Inference Kernel Contracts: Bounding Divergence in Post-Training and Deployment](https://mlsanity.com/paper/2606.07581/) (2026)

## Abstract (arXiv)

This paper provides a self-contained, from-scratch, exposition of key algorithms for instruction tuning of models: SFT, Rejection Sampling, REINFORCE, Trust Region Policy Optimization (TRPO), Proximal Policy Optimization (PPO), Group Relative Policy Optimization (GRPO), and Direct Preference Optimization (DPO). Explanations of these algorithms often assume prior knowledge, lack critical details, and/or are overly generalized and complex. Here, each method is discussed and developed step by step using simplified and explicit notation focused on LLMs, aiming to eliminate ambiguity and provide a clear and intuitive understanding of the concepts. By minimizing detours into the broader RL literature and connecting concepts to LLMs, we eliminate superfluous abstractions and reduce cognitive overhead. Following this exposition, we provide a literature review of new techniques and approaches beyond those detailed. Finally, new ideas for research and exploration in the form of GRAPE (Generalized Relative Advantage Policy Evolution) are presented.