Performance of Best of N Baseline for Various N and Sample Responses and GPT-4 Judgments

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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.

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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

Additional Empirical Results

D.1 Performance of Best of N baseline for Various N

We find that the Best of N baseline is a strong (although computationally expensive, requiring sampling many times) baseline in our experiments. We include an evaluation of the Best of N baseline for various N for the Anthropic-HH dialogue and TL;DR summarization; the results are shown in Figure 4.

D.2 Sample Responses and GPT-4 Judgments

In this section, we present examples of comparisons between DPO and the baseline (PPO temp 0. for summarization, and the ground truth chosen response for dialogue). See Tables 4-6 for summarization examples, and Tables 7-10 for dialogue examples.

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This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license.

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