Understanding RL for model training, and future directions with GRAPE (arxiv.org)

This paper delivers a compact, from‑scratch tutorial and synthesis of reinforcement‑learning methods used for instruction tuning of large language models, walking readers through SFT, Rejection Sampling, REINFORCE, TRPO, PPO, Group Relative Policy Optimization (GRPO), and Direct Preference Optimization (DPO). Rather than assuming RL background or hiding implementation details in general RL formalism, the authors rederive each algorithm with simplified, explicit notation tailored to LLMs, reducing abstraction and ambiguity. The result is a practical reference that codifies the core math and update rules practitioners need to implement or compare instruction‑tuning pipelines, with accompanying code and demos linked from the submission. Beyond exposition, the paper surveys recent advances and proposes GRAPE (Generalized Relative Advantage Policy Evolution) as a research direction that generalizes relative‑advantage style updates for more stable or flexible policy evolution in preference‑based training. While no empirical claims are made in the abstract, GRAPE is positioned as a unifying conceptual framework that could improve sample efficiency, stability of updates, and the integration of preference models with trust‑region or proximal constraints. For researchers and engineers working on RLHF, preference learning, or LLM fine‑tuning, this work clarifies trade‑offs between approaches (e.g., policy gradients vs trust‑region/proximal methods) and supplies a concrete foundation for experimentation and algorithmic refinement.