Authors:
(1) Rafael Rafailo, Stanford University and Equal contribution; more junior authors listed earlier;
(2) Archit Sharma, Stanford University and Equal contribution; more junior authors listed earlier;
(3) Eric Mitchel, Stanford University and Equal contribution; more junior authors listed earlier;
(4) Stefano Ermon, CZ Biohub;
(5) Christopher D. Manning, Stanford University;
(6) Chelsea Finn, Stanford University. Table of Links Abstract and 1. Introduction 2 Related Work 3 Preliminaries 4 Direct Preference Optimization 5 Theoretical Analysis of DPO 6 Experiments 7 Discussion, Acknowledgements, and References Author Contributions A Mathematical Derivations A.1 Deriving the Optimum of the KL-Constrained Reward Maximization Objective A.2 Deriving the DPO Objective Under the Bradley-Terry Model A.3 Deriving the DPO Objective Under the Plackett-Luce Model A.4 Deriving the Gradient of the DPO Objective and A.5 Proof of Lemma 1 and 2 A.6 Proof of Theorem 1 B DPO Implementation Details and Hyperparameters C Further Details on the Experimental Set-Up and C.1 IMDb Sentiment Experiment and Baseline Details C.2 GPT-4 prompts for computing summarization and dialogue win rates C.3 Unlikelihood baseline D Additional Empirical Results D.1 Performance of Best of N baseline for Various N and D.2 Sample Responses and GPT-4 Judgments D.3 Human study details C Further Details on the Experimental Set-Up In this section, we include additional details relevant to our experimental design. C.1 IMDb Sentiment Experiment and Baseline Details The prompts are prefixes from the IMDB dataset of length 2-8 tokens. We use the pre-trained sentiment classifier siebert/sentiment-roberta-large-english as a ground-truth reward model and gpt2-large as a base model. We use these larger models as we found the default ones to generate low-quality text and rewards to be somewhat inaccurate. We first use supervised fine-tuning on a subset of the IMDB data for 1 epoch. We then use this model to sample 4 completions for 25000 prefixes and create 6 preference pairs for each prefix using the ground-truth reward model. The RLHF reward model is initialized from the gpt2-large model and trained for 3 epochs on the preference datasets, and we take the checkpoint with the highest validation set accuracy. The “TRL” run uses the hyper-parameters in the TRL library. Our implementation uses larger batch samples of 1024 per PPO step. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Authors: (1) Rafael Rafailo, Stanford University and Equal contribution; more junior authors listed earlier; (2) Archit Sharma, Stanford University and Equal contribution; more junior authors listed earlier; (3) Eric Mitchel, Stanford University and Equal contribution; more junior authors listed earlier; (4) Stefano Ermon, CZ Biohub; (5) Christopher D. Manning, Stanford University; (6) Chelsea Finn, Stanford University. Authors: Authors: (1) Rafael Rafailo, Stanford University and Equal contribution; more junior authors listed earlier; (2) Archit Sharma, Stanford University and Equal contribution; more junior authors listed earlier; (3) Eric Mitchel, Stanford University and Equal contribution; more junior authors listed earlier; (4) Stefano Ermon, CZ Biohub; (5) Christopher D. Manning, Stanford University; (6) Chelsea Finn, Stanford University. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2 Related Work 2 Related Work 3 Preliminaries 3 Preliminaries 4 Direct Preference Optimization 4 Direct Preference Optimization 5 Theoretical Analysis of DPO 5 Theoretical Analysis of DPO 6 Experiments 6 Experiments 7 Discussion, Acknowledgements, and References 7 Discussion, Acknowledgements, and References Author Contributions Author Contributions A Mathematical Derivations A.1 Deriving the Optimum of the KL-Constrained Reward Maximization Objective A.1 Deriving the Optimum of the KL-Constrained Reward Maximization Objective A.2 Deriving the DPO Objective Under the Bradley-Terry Model A.2 Deriving the DPO Objective Under the Bradley-Terry Model A.3 Deriving the DPO Objective Under the Plackett-Luce Model A.3 Deriving the DPO Objective Under the Plackett-Luce Model A.4 Deriving the Gradient of the DPO Objective and A.5 Proof of Lemma 1 and 2 A.4 Deriving the Gradient of the DPO Objective and A.5 Proof of Lemma 1 and 2 A.6 Proof of Theorem 1 A.6 Proof of Theorem 1 B DPO Implementation Details and Hyperparameters B DPO Implementation Details and Hyperparameters C Further Details on the Experimental Set-Up and C.1 IMDb Sentiment Experiment and Baseline Details C Further Details on the Experimental Set-Up and C.1 IMDb Sentiment Experiment and Baseline Details C.2 GPT-4 prompts for computing summarization and dialogue win rates C.2 GPT-4 prompts for computing summarization and dialogue win rates C.3 Unlikelihood baseline C.3 Unlikelihood baseline D Additional Empirical Results D.1 Performance of Best of N baseline for Various N and D.2 Sample Responses and GPT-4 Judgments D.1 Performance of Best of N baseline for Various N and D.2 Sample Responses and GPT-4 Judgments D.3 Human study details D.3 Human study details C Further Details on the Experimental Set-Up In this section, we include additional details relevant to our experimental design. C.1 IMDb Sentiment Experiment and Baseline Details The prompts are prefixes from the IMDB dataset of length 2-8 tokens. We use the pre-trained sentiment classifier siebert/sentiment-roberta-large-english as a ground-truth reward model and gpt2-large as a base model. We use these larger models as we found the default ones to generate low-quality text and rewards to be somewhat inaccurate. We first use supervised fine-tuning on a subset of the IMDB data for 1 epoch. We then use this model to sample 4 completions for 25000 prefixes and create 6 preference pairs for each prefix using the ground-truth reward model. The RLHF reward model is initialized from the gpt2-large model and trained for 3 epochs on the preference datasets, and we take the checkpoint with the highest validation set accuracy. The “TRL” run uses the hyper-parameters in the TRL library. Our implementation uses larger batch samples of 1024 per PPO step. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. available on arxiv

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