Direct Preference Optimization (DPO) explained: Bradley-Terry model, log probabilities, math

In this video I will explain Direct Preference Optimization (DPO), an alignment technique for language models introduced in the paper "Direct Preference Optimization: Your Language Model is Secretly a Reward Model". I start by introducing language models and how they are used for text generation. After briefly introducing the topic of AI alignment, I start by reviewing Reinforcement Learning (RL), a topic that is necessary to understand the reward model and its loss function. I derive step by step the loss function of the reward model under the Bradley-Terry model of preferences, a derivation that is missing in the DPO paper. Using the Bradley-Terry model, I build the loss of the DPO algorithm, not only explaining its math derivation, but also giving intuition on how it works. In the last part, I describe how to use the loss practically, that is, how to calculate the log probabilities using a Transformer model, by showing how it is implemented in the Hugging Face library. DPO paper: Rafailov, R., Sharma, A., Mitchell, E., Manning, C.D., Ermon, S. and Finn, C., 2024. Direct preference optimization: Your language model is secretly a reward model. Advances in Neural Information Processing Systems, 36. https://arxiv.org/abs/2305.18290 If you're interested in how to derive the optimal solution to the RL constrained optimization problem, I highly recommend the following paper (Appendinx A, equation 36): Peng XB, Kumar A, Zhang G, Levine S. Advantage-weighted regression: Simple and scalable off-policy reinforcement learning. arXiv preprint arXiv:1910.00177. 2019 Oct 1. https://arxiv.org/abs/1910.00177 Slides PDF: https://github.com/hkproj/dpo-notes Chapters 00:00:00 - Introduction 00:02:10 - Intro to Language Models 00:04:08 - AI Alignment 00:05:11 - Intro to RL 00:08:19 - RL for Language Models 00:10:44 - Reward model 00:13:07 - The Bradley-Terry model 00:21:34 - Optimization Objective 00:29:52 - DPO: deriving its loss 00:41:05 - Computing the log probabilities 00:47: