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

Rohit Patel

TL;DR

The paper surveys the landscape of reinforcement learning for model training (RLMT), tracing a trajectory from supervised fine-tuning (SFT) and rejection sampling to policy-based methods such as REINFORCE, TRPO, PPO, GRPO, and DPO, all with an LLM-centric, first-principles treatment. It emphasizes practical, implementable formulations, clear connections to next-token generation, and stability mechanisms (baselines, KL penalties, clipping) while highlighting limitations of prior approaches (e.g., data efficiency, model collapse). Beyond established methods, the authors discuss emerging directions (RLAIF, curriculum learning, process supervision, self-play, debates, offline RL) and introduce GRAPE—a generalized framework that leverages modular rubrics, critiques, and optional reward models for scalable, transparent model alignment. The work aims to provide a concrete, scalable roadmap for aligning large language models with human intent through progressively more nuanced feedback signals and iterative improvement, with GRAPE offering a flexible, plug-in approach for future research and deployment.

Abstract

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.

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

TL;DR

The paper surveys the landscape of reinforcement learning for model training (RLMT), tracing a trajectory from supervised fine-tuning (SFT) and rejection sampling to policy-based methods such as REINFORCE, TRPO, PPO, GRPO, and DPO, all with an LLM-centric, first-principles treatment. It emphasizes practical, implementable formulations, clear connections to next-token generation, and stability mechanisms (baselines, KL penalties, clipping) while highlighting limitations of prior approaches (e.g., data efficiency, model collapse). Beyond established methods, the authors discuss emerging directions (RLAIF, curriculum learning, process supervision, self-play, debates, offline RL) and introduce GRAPE—a generalized framework that leverages modular rubrics, critiques, and optional reward models for scalable, transparent model alignment. The work aims to provide a concrete, scalable roadmap for aligning large language models with human intent through progressively more nuanced feedback signals and iterative improvement, with GRAPE offering a flexible, plug-in approach for future research and deployment.

Abstract

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.

Paper Structure

This paper contains 31 sections, 1 theorem, 50 equations, 1 figure, 2 tables.

Table of Contents

  1. Instruction tuning models
  2. Supervised fine tuning
  3. Rejection Sampling
  4. Reinforcement learning
  5. REINFORCE
  6. Value function
  7. Advantage function
  8. Reward model
  9. Trust Region Policy Optimization
  10. Proximal Policy Optimization
  11. Loss function used in practice
  12. Group Relative Policy Optimization
  13. Direct Preference Optimization
  14. Emerging approaches
  15. Curriculum learning
  16. ...and 16 more sections

Key Result

Lemma 8.1

If we have a sample of $\rho$ observations, $\tau_i, i \in 1,...\rho$, each with standard deviation $\sigma_i$ and we have $\bar{\varphi}_i$ inversely proportional to variance of the corresponding $\tau_i$, then:

Figures (1)

  • Figure 1: Recursively feeding generated tokens to LLMs for longer text generation

Theorems & Definitions (2)

  • Lemma 8.1
  • proof