🤖 AI Summary
Existing LLM instruction-tuning algorithms—such as supervised fine-tuning (SFT), proximal policy optimization (PPO), and direct preference optimization (DPO)—are often explained with heavy reliance on prior knowledge, omit critical derivations, or remain overly abstract, resulting in high cognitive barriers and poor interpretability.
Method: This paper systematically unifies mainstream reinforcement learning and preference optimization approaches under a concise, symbolically grounded derivation framework explicitly tailored to practical LLM training scenarios.
Contribution/Results: We introduce GRAPE (Generalized Relative Advantage Policy Evolution), a novel paradigm for future preference learning designed to overcome fundamental limitations of current methods in objective design, training stability, and generalization. The framework provides a coherent, step-by-step exposition—from SFT through DPO—enhancing algorithmic intuition and theoretical transparency. It establishes a rigorous foundation for advancing preference-based LLM alignment and offers principled directions for subsequent research.
📝 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.