Discussion, Acknowledgements, and References

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

7 Discussion

Learning from preferences is a powerful, scalable framework for training capable, aligned language models. We have introduced DPO, a simple training paradigm for training language models from preferences without reinforcement learning. Rather than coercing the preference learning problem into a standard RL setting in order to use off-the-shelf RL algorithms, DPO identifies a mapping between language model policies and reward functions that enables training a language model to satisfy human preferences directly, with a simple cross-entropy loss, without reinforcement learning or loss of generality. With virtually no tuning of hyperparameters, DPO performs similarly or better than existing RLHF algorithms, including those based on PPO; DPO thus meaningfully reduces the barrier to training more language models from human preferences.

Limitations & Future Work. Our results raise several important questions for future work. How does the DPO policy generalize out of distribution, compared with learning from an explicit reward function? Our initial results suggest that DPO policies can generalize similarly to PPO-based models, but more comprehensive study is needed. For example, can training with self-labeling from the DPO policy similarly make effective use of unlabeled prompts? On another front, how does reward over-optimization manifest in the direct preference optimization setting, and is the slight decrease in performance in Figure 3-right an instance of it? Additionally, while we evaluate models up to 6B parameters, exploration of scaling DPO to state-of-the-art models orders of magnitude larger is an exciting direction for future work. Regarding evaluations, we find that the win rates computed by GPT-4 are impacted by the prompt; future work may study the best way to elicit high-quality judgments from automated systems. Finally, many possible applications of DPO exist beyond training language models from human preferences, including training generative models in other modalities.

Acknowledgements

EM gratefully acknowledges funding from a Knight-Hennessy Graduate Fellowship. CF and CM are CIFAR Fellows. This work was supported in part by the Stanford Accelerator for Learning (SAL) and Stanford Institute for Human-Centered Artificial Intelligence (HAI) Generative AI for the Future of Learning seed grant program. The Stanford Center for Research on Foundation Models (CRFM) provided part of the compute resources used for the experiments in this work. This work was supported in part by ONR grant N00014-20-1-2675.

References

[1] Y. Bai, A. Jones, K. Ndousse, A. Askell, A. Chen, N. DasSarma, D. Drain, S. Fort, D. Ganguli, T. Henighan, N. Joseph, S. Kadavath, J. Kernion, T. Conerly, S. El-Showk, N. Elhage, Z. HatfieldDodds, D. Hernandez, T. Hume, S. Johnston, S. Kravec, L. Lovitt, N. Nanda, C. Olsson, D. Amodei, T. Brown, J. Clark, S. McCandlish, C. Olah, B. Mann, and J. Kaplan. Training a helpful and harmless assistant with reinforcement learning from human feedback, 2022.

[2] Y. Bai, S. Kadavath, S. Kundu, A. Askell, J. Kernion, A. Jones, A. Chen, A. Goldie, A. Mirhoseini, C. McKinnon, C. Chen, C. Olsson, C. Olah, D. Hernandez, D. Drain, D. Ganguli, D. Li, E. Tran-Johnson, E. Perez, J. Kerr, J. Mueller, J. Ladish, J. Landau, K. Ndousse, K. Lukosuite, L. Lovitt, M. Sellitto, N. Elhage, N. Schiefer, N. Mercado, N. DasSarma, R. Lasenby, R. Larson, S. Ringer, S. Johnston, S. Kravec, S. E. Showk, S. Fort, T. Lanham, T. Telleen-Lawton, T. Conerly, T. Henighan, T. Hume, S. R. Bowman, Z. Hatfield-Dodds, B. Mann, D. Amodei, N. Joseph, S. McCandlish, T. Brown, and J. Kaplan. Constitutional ai: Harmlessness from ai feedback, 2022.

[3] S. Biderman, H. Schoelkopf, Q. Anthony, H. Bradley, K. O’Brien, E. Hallahan, M. A. Khan, S. Purohit, U. S. Prashanth, E. Raff, A. Skowron, L. Sutawika, and O. van der Wal. Pythia: A suite for analyzing large language models across training and scaling, 2023.

[4] H. Bong and A. Rinaldo. Generalized results for the existence and consistency of the MLE in the Bradley-Terry-Luce model. International Conference on Machine Learning, 2022. arXiv:2110.11487.

[5] R. A. Bradley and M. E. Terry. Rank analysis of incomplete block designs: I. the method of paired comparisons. Biometrika, 39(3/4):324–345, 1952. doi: https://doi.org/10.2307/2334029.

[6] T. Brown, B. Mann, N. Ryder, M. Subbiah, J. D. Kaplan, P. Dhariwal, A. Neelakantan, P. Shyam, G. Sastry, A. Askell, S. Agarwal, A. Herbert-Voss, G. Krueger, T. Henighan, R. Child, A. Ramesh, D. Ziegler, J. Wu, C. Winter, C. Hesse, M. Chen, E. Sigler, M. Litwin, S. Gray, B. Chess, J. Clark, C. Berner, S. McCandlish, A. Radford, I. Sutskever, and D. Amodei. Language models are few-shot learners. In H. Larochelle, M. Ranzato, R. Hadsell, M. Balcan, and H. Lin, editors, Advances in Neural Information Processing Systems, volume 33, pages 1877– 1901. Curran Associates, Inc., 2020. URL https://proceedings.neurips.cc/paper_ files/paper/2020/file/1457c0d6bfcb4967418bfb8ac142f64a-Paper.pdf.

[7] T. Brown, B. Mann, N. Ryder, M. Subbiah, J. D. Kaplan, P. Dhariwal, A. Neelakantan, P. Shyam, G. Sastry, A. Askell, et al. Language models are few-shot learners. Advances in neural information processing systems, 33:1877–1901, 2020.

[8] S. Bubeck, V. Chandrasekaran, R. Eldan, J. Gehrke, E. Horvitz, E. Kamar, P. Lee, Y. T. Lee, Y. Li, S. Lundberg, H. Nori, H. Palangi, M. T. Ribeiro, and Y. Zhang. Sparks of artificial general intelligence: Early experiments with GPT-4, 2023. arXiv preprint arXiv:2303.12712.

[9] R. Busa-Fekete, B. Szörényi, P. Weng, W. Cheng, and E. Hüllermeier. Preference-based reinforcement learning: evolutionary direct policy search using a preference-based racing algorithm. Machine Learning, 97(3):327–351, July 2014. doi: 10.1007/s10994-014-5458-8. URL https://doi.org/10.1007/s10994-014-5458-8.

[10] Y. Chen, R. Wang, H. Jiang, S. Shi, and R.-L. Xu. Exploring the use of large language models for reference-free text quality evaluation: A preliminary empirical study. ArXiv, abs/2304.00723, 2023.

[11] A. Chowdhery, S. Narang, J. Devlin, M. Bosma, G. Mishra, A. Roberts, P. Barham, H. W. Chung, C. Sutton, S. Gehrmann, et al. Palm: Scaling language modeling with pathways. arXiv preprint arXiv:2204.02311, 2022.

[12] P. F. Christiano, J. Leike, T. Brown, M. Martic, S. Legg, and D. Amodei. Deep reinforcement learning from human preferences. In I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 30. Curran Associates, Inc., 2017. URL https://proceedings.neurips.cc/ paper_files/paper/2017/file/d5e2c0adad503c91f91df240d0cd4e49-Paper.pdf.

[13] H. W. Chung, L. Hou, S. Longpre, B. Zoph, Y. Tay, W. Fedus, Y. Li, X. Wang, M. Dehghani, S. Brahma, A. Webson, S. S. Gu, Z. Dai, M. Suzgun, X. Chen, A. Chowdhery, A. Castro-Ros, M. Pellat, K. Robinson, D. Valter, S. Narang, G. Mishra, A. Yu, V. Zhao, Y. Huang, A. Dai, H. Yu, S. Petrov, E. H. Chi, J. Dean, J. Devlin, A. Roberts, D. Zhou, Q. V. Le, and J. Wei. Scaling instruction-finetuned language models, 2022.

[14] M. Dudík, K. Hofmann, R. E. Schapire, A. Slivkins, and M. Zoghi. Contextual dueling bandits. In P. Grünwald, E. Hazan, and S. Kale, editors, Proceedings of The 28th Conference on Learning Theory, volume 40 of Proceedings of Machine Learning Research, pages 563–587, Paris, France, 03–06 Jul 2015. PMLR. URL https://proceedings.mlr.press/v40/Dudik15.html.

[15] D. Go, T. Korbak, G. Kruszewski, J. Rozen, N. Ryu, and M. Dymetman. Aligning language models with preferences through f-divergence minimization. In Proceedings of the 40th International Conference on Machine Learning, ICML’23. JMLR.org, 2023.

[16] A. Jain, B. Wojcik, T. Joachims, and A. Saxena. Learning trajectory preferences for manipulators via iterative improvement. In C. Burges, L. Bottou, M. Welling, Z. Ghahramani, and K. Weinberger, editors, Advances in Neural Information Processing Systems, volume 26. Curran Associates, Inc., 2013. URL https://proceedings.neurips.cc/paper_files/paper/ 2013/file/c058f544c737782deacefa532d9add4c-Paper.pdf.

[17] T. Korbak, H. Elsahar, G. Kruszewski, and M. Dymetman. On reinforcement learning and distribution matching for fine-tuning language models with no catastrophic forgetting. In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh, editors, Advances in Neural Information Processing Systems, volume 35, pages 16203–16220. Curran Associates, Inc., 2022. URL https://proceedings.neurips.cc/paper_files/paper/2022/file/ 67496dfa96afddab795530cc7c69b57a-Paper-Conference.pdf.

[18] J. Kreutzer, J. Uyheng, and S. Riezler. Reliability and learnability of human bandit feedback for sequence-to-sequence reinforcement learning. In Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 1777–1788, Melbourne, Australia, July 2018. Association for Computational Linguistics. doi: 10.18653/v1/ P18-1165. URL https://aclanthology.org/P18-1165.

[19] A. Kupcsik, D. Hsu, and W. S. Lee. Learning Dynamic Robot-to-Human Object Handover from Human Feedback, pages 161–176. Springer International Publishing, 01 2018. ISBN 978-3-319-51531-1. doi: 10.1007/978-3-319-51532-8_10.

[20] S. Levine. Reinforcement learning and control as probabilistic inference: Tutorial and review, 2018.

[21] R. D. Luce. Individual choice behavior: A theoretical analysis. Courier Corporation, 2012.

[22] A. L. Maas, R. E. Daly, P. T. Pham, D. Huang, A. Y. Ng, and C. Potts. Learning word vectors for sentiment analysis. In Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Human Language Technologies, pages 142–150, Portland, Oregon, USA, June 2011. Association for Computational Linguistics. URL http://www.aclweb.org/ anthology/P11-1015.

[23] S. Mishra, D. Khashabi, C. Baral, and H. Hajishirzi. Cross-task generalization via natural language crowdsourcing instructions. In Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 3470–3487, Dublin, Ireland, May 2022. Association for Computational Linguistics. doi: 10.18653/v1/2022.acl-long. 244. URL https://aclanthology.org/2022.acl-long.244.

[24] R. Nallapati, B. Zhou, C. dos Santos, Ç. Gulçehre, and B. Xiang. Abstractive text summarization using sequence-to-sequence RNNs and beyond. In Proceedings of the 20th SIGNLL Conference on Computational Natural Language Learning, pages 280–290, Berlin, Germany, Aug. 2016. Association for Computational Linguistics. doi: 10.18653/v1/K16-1028. URL https:// aclanthology.org/K16-1028.

[25] D. Narayanan, M. Shoeybi, J. Casper, P. LeGresley, M. Patwary, V. Korthikanti, D. Vainbrand, P. Kashinkunti, J. Bernauer, B. Catanzaro, A. Phanishayee, and M. Zaharia. Efficient large-scale language model training on gpu clusters using megatron-lm. In Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, SC ’21, New York, NY, USA, 2021. Association for Computing Machinery. ISBN 9781450384421. doi: 10.1145/3458817.3476209. URL https://doi.org/10.1145/3458817.3476209.

[26] L. Ouyang, J. Wu, X. Jiang, D. Almeida, C. Wainwright, P. Mishkin, C. Zhang, S. Agarwal, K. Slama, A. Ray, J. Schulman, J. Hilton, F. Kelton, L. Miller, M. Simens, A. Askell, P. Welinder, P. F. Christiano, J. Leike, and R. Lowe. Training language models to follow instructions with human feedback. In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh, editors, Advances in Neural Information Processing Systems, volume 35, pages 27730–27744. Curran Associates, Inc., 2022. URL https://proceedings.neurips.cc/paper_files/ paper/2022/file/b1efde53be364a73914f58805a001731-Paper-Conference.pdf.

[27] R. Paulus, C. Xiong, and R. Socher. A deep reinforced model for abstractive summarization. In International Conference on Learning Representations, 2018. URL https://openreview. net/forum?id=HkAClQgA-.

[28] X. B. Peng, A. Kumar, G. Zhang, and S. Levine. Advantage-weighted regression: Simple and scalable off-policy reinforcement learning. arXiv preprint arXiv:1910.00177, 2019.

[29] J. Peters and S. Schaal. Reinforcement learning by reward-weighted regression for operational space control. In Proceedings of the 24th international conference on Machine learning, pages 745–750, 2007.

[30] R. L. Plackett. The analysis of permutations. Journal of the Royal Statistical Society. Series C (Applied Statistics), 24(2):193–202, 1975. doi: https://doi.org/10.2307/2346567.

[31] A. Radford, J. Wu, R. Child, D. Luan, D. Amodei, and I. Sutskever. Language models are unsupervised multitask learners, 2019. Ms., OpenAI.

[32] R. Ramamurthy, P. Ammanabrolu, K. Brantley, J. Hessel, R. Sifa, C. Bauckhage, H. Hajishirzi, and Y. Choi. Is reinforcement learning (not) for natural language processing: Benchmarks, baselines, and building blocks for natural language policy optimization. In The Eleventh International Conference on Learning Representations, 2023. URL https://openreview. net/forum?id=8aHzds2uUyB.

[33] M. Ranzato, S. Chopra, M. Auli, and W. Zaremba. Sequence level training with recurrent neural networks. CoRR, abs/1511.06732, 2015.

[34] D. Sadigh, A. D. Dragan, S. Sastry, and S. A. Seshia. Active preference-based learning of reward functions. In Robotics: Science and Systems (RSS), 2017.

[35] A. Saha, A. Pacchiano, and J. Lee. Dueling rl: Reinforcement learning with trajectory preferences. In F. Ruiz, J. Dy, and J.-W. van de Meent, editors, Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, volume 206 of Proceedings of Machine Learning Research, pages 6263–6289. PMLR, 25–27 Apr 2023. URL https://proceedings.mlr.press/v206/saha23a.html.

[36] V. Sanh, A. Webson, C. Raffel, S. Bach, L. Sutawika, Z. Alyafeai, A. Chaffin, A. Stiegler, A. Raja, M. Dey, M. S. Bari, C. Xu, U. Thakker, S. S. Sharma, E. Szczechla, T. Kim, G. Chhablani, N. Nayak, D. Datta, J. Chang, M. T.-J. Jiang, H. Wang, M. Manica, S. Shen, Z. X. Yong, H. Pandey, R. Bawden, T. Wang, T. Neeraj, J. Rozen, A. Sharma, A. Santilli, T. Fevry, J. A. Fries, R. Teehan, T. L. Scao, S. Biderman, L. Gao, T. Wolf, and A. M. Rush. Multitask prompted training enables zero-shot task generalization. In International Conference on Learning Representations, 2022. URL https://openreview.net/forum?id=9Vrb9D0WI4.

[37] J. Schulman, F. Wolski, P. Dhariwal, A. Radford, and O. Klimov. Proximal policy optimization algorithms, 2017. [38] N. Stiennon, L. Ouyang, J. Wu, D. M. Ziegler, R. Lowe, C. Voss, A. Radford, D. Amodei, and P. Christiano. Learning to summarize from human feedback, 2022.

[39] R. Thoppilan, D. D. Freitas, J. Hall, N. Shazeer, A. Kulshreshtha, H.-T. Cheng, A. Jin, T. Bos, L. Baker, Y. Du, Y. Li, H. Lee, H. S. Zheng, A. Ghafouri, M. Menegali, Y. Huang, M. Krikun, D. Lepikhin, J. Qin, D. Chen, Y. Xu, Z. Chen, A. Roberts, M. Bosma, V. Zhao, Y. Zhou, C.-C. Chang, I. Krivokon, W. Rusch, M. Pickett, P. Srinivasan, L. Man, K. Meier-Hellstern, M. R. Morris, T. Doshi, R. D. Santos, T. Duke, J. Soraker, B. Zevenbergen, V. Prabhakaran, M. Diaz, B. Hutchinson, K. Olson, A. Molina, E. Hoffman-John, J. Lee, L. Aroyo, R. Rajakumar, A. Butryna, M. Lamm, V. Kuzmina, J. Fenton, A. Cohen, R. Bernstein, R. Kurzweil, B. AgueraArcas, C. Cui, M. Croak, E. Chi, and Q. Le. Lamda: Language models for dialog applications, 2022.

[40] H. Touvron, T. Lavril, G. Izacard, X. Martinet, M.-A. Lachaux, T. Lacroix, B. Rozière, N. Goyal, E. Hambro, F. Azhar, et al. Llama: Open and efficient foundation language models. arXiv preprint arXiv:2302.13971, 2023.

[41] M. Völske, M. Potthast, S. Syed, and B. Stein. TL;DR: Mining Reddit to learn automatic summarization. In Proceedings of the Workshop on New Frontiers in Summarization, pages 59–63, Copenhagen, Denmark, Sept. 2017. Association for Computational Linguistics. doi: 10.18653/v1/W17-4508. URL https://aclanthology.org/W17-4508.

[42] L. von Werra, J. Tow, reciprocated, S. Matiana, A. Havrilla, cat state, L. Castricato, Alan, D. V. Phung, A. Thakur, A. Bukhtiyarov, aaronrmm, F. Milo, Daniel, D. King, D. Shin, E. Kim, J. Wei, M. Romero, N. Pochinkov, O. Sanseviero, R. Adithyan, S. Siu, T. Simonini, V. Blagojevic, X. Song, Z. Witten, alexandremuzio, and crumb. CarperAI/trlx: v0.6.0: LLaMa (Alpaca), Benchmark Util, T5 ILQL, Tests, Mar. 2023. URL https://doi.org/10.5281/zenodo. 7790115.

[43] B. Wang and A. Komatsuzaki. GPT-J-6B: A 6 Billion Parameter Autoregressive Language Model. https://github.com/kingoflolz/mesh-transformer-jax, May 2021.

[44] S. Welleck, I. Kulikov, S. Roller, E. Dinan, K. Cho, and J. Weston. Neural text generation with unlikelihood training. arXiv preprint arXiv:1908.04319, 2019.

[45] R. J. Williams. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Mach. Learn., 8(3–4):229–256, may 1992. ISSN 0885-6125. doi: 10.1007/BF00992696. URL https://doi.org/10.1007/BF00992696.

[46] Y. Wu and B. Hu. Learning to extract coherent summary via deep reinforcement learning. In Proceedings of the Thirty-Second AAAI Conference on Artificial Intelligence and Thirtieth Innovative Applications of Artificial Intelligence Conference and Eighth AAAI Symposium on Educational Advances in Artificial Intelligence, AAAI’18/IAAI’18/EAAI’18. AAAI Press, 2018. ISBN 978-1-57735-800-8.

[47] X. Yan, C. Luo, C. L. A. Clarke, N. Craswell, E. M. Voorhees, and P. Castells. Human preferences as dueling bandits. In Proceedings of the 45th International ACM SIGIR Conference on Research and Development in Information Retrieval, SIGIR ’22, page 567–577, New York, NY, USA, 2022. Association for Computing Machinery. ISBN 9781450387323. doi: 10.1145/3477495.3531991. URL https://doi.org/10.1145/3477495.3531991.

[48] Y. Yue, J. Broder, R. Kleinberg, and T. Joachims. The k-armed dueling bandits problem. Journal of Computer and System Sciences, 78(5):1538–1556, 2012. ISSN 0022-0000. doi: https: //doi.org/10.1016/j.jcss.2011.12.028. URL https://www.sciencedirect.com/science/ article/pii/S0022000012000281. JCSS Special Issue: Cloud Computing 2011.

[49] D. M. Ziegler, N. Stiennon, J. Wu, T. B. Brown, A. Radford, D. Amodei, P. Christiano, and G. Irving. Fine-tuning language models from human preferences, 2020.