Capstone Lesson 40: Direct Preference Optimization from Scratch

Reward models and PPO are the classical RLHF stack. DPO collapses that stack into a single supervised loss that fits a policy directly against preference pairs. This lesson derives the DPO loss from the reward-difference identity, ships a working reference model plus policy model, computes per-token log-probabilities, and trains a tiny transformer on a preference fixture of chosen and rejected completions. Tests pin the loss math and the gradient direction so you know the implementation matches the paper.