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

6 Experiments

In this section, we empirically evaluate DPO’s ability to train policies directly from preferences. First, in a well-controlled text-generation setting, we ask: how efficiently does DPO trade off maximizing reward and minimizing KL-divergence with the reference policy, compared to common preference learning algorithms such as PPO? Next, we evaluate DPO’s performance on larger models and more difficult RLHF tasks, including summarization and dialogue. We find that with almost no tuning of hyperparameters, DPO tends to perform as well or better than strong baselines like RLHF with PPO as well as returning the best of N sampled trajectories under a learned reward function. Before presenting these results, we describe the experimental set-up; additional details are in Appendix C.

Evaluation. Our experiments use two different approaches to evaluation. In order to analyze the effectiveness of each algorithm in optimizing the constrained reward maximization objective, in the controlled sentiment generation setting we evaluate each algorithm by its frontier of achieved reward and KL-divergence from the reference policy; this frontier is computable because we have access to the ground-truth reward function (a sentiment classifier). However, in the real world, the ground truth reward function is not known; therefore, we evaluate algorithms with their win rate against a baseline policy, using GPT-4 as a proxy for human evaluation of summary quality and response helpfulness in the summarization and single-turn dialogue settings, respectively. For summarization, we use reference summaries in the test set as the baseline; for dialogue, we use the preferred response in the

test dataset as the baseline. While existing studies suggest LMs can be better automated evaluators than existing metrics [10], we conduct a human study to justify our usage of GPT-4 for evaluation in Sec. 6.4. We find GPT-4 judgments correlate strongly with humans, with human agreement with GPT-4 typically similar or higher than inter-human annotator agreement.

6.1 How well can DPO optimize the RLHF objective?

6.2 Can DPO scale to real preference datasets?

Next, we evaluate fine-tuning performance of DPO on summarization and single-turn dialogue. For summarization, automatic evaluation metrics such as ROUGE can be poorly correlated with human preferences [38], and prior work has found that fine-tuning LMs using PPO on human preferences to provide more effective summaries. We evaluate different methods by sampling completions on the test split of TL;DR summarization dataset, and computing the average win rate against reference completions in the test set. The completions for all methods are sampled at temperatures varying from 0.0 to 1.0, and the win rates are shown in Figure 2 (right). DPO, PPO and Preferred-FT all fine-tune the same GPT-J SFT model[4]. We find that DPO has a win rate of approximately 61% at a temperature of 0.0, exceeding the performance of PPO at 57% at its optimal sampling temperature of 0.0. DPO also achieves a higher maximum win rate compared to the best of N baseline. We note that we did not meaningfully tune DPO’s β hyperparameter, so these results may underestimate DPO’s potential. Moreover, we find DPO to be much more robust to the sampling temperature than PPO, the performance of which can degrade to that of the base GPT-J model at high temperatures. Preferred-FT does not improve significantly over the SFT model. We also compare DPO and PPO head-to-head in human evaluations in Section 6.4, where DPO samples at temperature 0.25 were preferred 58% times over PPO samples at temperature 0.

On single-turn dialogue, we evaluate the different methods on the subset of the test split of the Anthropic HH dataset [1] with one step of human-assistant interaction. GPT-4 evaluations use the preferred completions on the test as the reference to compute the win rate for different methods. As there is no standard SFT model for this task, we start with a pre-trained Pythia-2.8B, use Preferred-FT to train a reference model on the chosen completions such that completions are within distribution of the model, and then train using DPO. We also compare against the best of 128 Preferred-FT completions (we found the Best of N baseline plateaus at 128 completions for this task; see Appendix Figure 4) and a 2-shot prompted version of the Pythia-2.8B base model, finding DPO performs as well or better for the best-performing temperatures for each method. We also evaluate an RLHF model trained with PPO on the Anthropic HH dataset [5] from a well-known source [6], but are unable to find a prompt or sampling temperature that gives performance better than the base Pythia-2.8B model. Based on our results from TL;DR and the fact that both methods optimize the same reward function, we consider Best of 128 a rough proxy for PPO-level performance. Overall, DPO is the only computationally efficient method that improves over the preferred completions in the Anthropic HH dataset, and provides similar or better performance to the computationally demanding Best of 128 baseline. Finally, Figure 3 shows that DPO converges to its best performance relatively quickly.

6.3 Generalization to a new input distribution

To further compare the performance of PPO and DPO under distribution shifts, we evaluate the PPO and DPO policies from our Reddit TL;DR summarization experiment on a different distribution, news articles in the test split of the CNN/DailyMail dataset [24], using the best sampling temperatures from TL;DR (0 and 0.25). The results are presented in Table 1. We computed the GPT-4 win rate against the ground-truth summaries in the datasets, using the same GPT4 (C) prompt we used for Reddit TL;DR, but replacing the words “forum post” with “news article”. For this new distribution, DPO continues to outperform the PPO policy by a significant margin. This experiment provides initial evidence that DPO policies can generalize similarly well to PPO policies, even though DPO does not use the additional unlabeled Reddit TL;DR prompts that PPO uses.

6.4 Validating GPT-4 judgments with human judgments

We conduct a human study to verify the reliability of GPT-4’s judgments, using the results of the TL;DR summarization experiment and two different GPT-4 prompts. The GPT-4 (S) (simple) prompt simply asks for which summary better-summarizes the important information in the post. The GPT-4 (C) (concise) prompt also asks for which summary is more concise; we evaluate this prompt because we find that GPT-4 prefers longer, more repetitive summaries than humans do with the GPT-4 (S) prompt. See Appendix C.2 for the complete prompts. We perform three comparisons, using the highest (DPO, temp. 0.25), the lowest (PPO, temp. 1.0), and a middle-performing (SFT, temp. 0.25) method with the aim of covering a diversity of sample qualities; all three methods are compared against greedily sampled PPO (its best-performing temperature). We find that with both prompts, GPT-4 tends to agree with humans about as often as humans agree with each other, suggesting that GPT-4 is a reasonable proxy for human evaluations (due to limited human raters, we only collect multiple human judgments for the DPO and PPO-1 comparisons). Overall, the GPT-4 (C) prompt generally provides win rates more representative of humans; we therefore use this prompt for the main results in Section 6.2. For additional details about the human study, including the web interface presented to raters and the list of human volunteers, see Appendix D.3.

[2] https://huggingface.co/CarperAI/openai_summarize_tldr_sft

[3] That is, the sum of the per-timestep KL-divergences.

[4] https://huggingface.co/CarperAI/openai_summarize_tldr_sft

[5] https://huggingface.co/reciprocate/ppo_hh_pythia-6B

[6] https://github.com/CarperAI/trlx/tree/main/examples/hh