Energy-Based Preference Model Offers Better Offline Alignment than the Bradley-Terry Preference Model

Yuzhong Hong, Hanshan Zhang, Junwei Bao, Hongfei Jiang, Yang Song
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:23787-23804, 2025.

Abstract

Since the debut of DPO, it has been shown that aligning a target LLM with human preferences via the KL-constrained RLHF loss is mathematically equivalent to a special kind of reward modeling task. Concretely, the task requires: 1) using the target LLM to parameterize the reward model, and 2) tuning the reward model so that it has a 1:1 linear relationship with the true reward. However, we identify a significant issue: the DPO loss might have multiple minimizers, of which only one satisfies the required linearity condition. The problem arises from a well-known issue of the underlying Bradley-Terry preference model: it does not always have a unique maximum likelihood estimator (MLE). Consequently, the minimizer of the RLHF loss might be unattainable because it is merely one among many minimizers of the DPO loss. As a better alternative, we propose an energy-based preference model (EBM) that always has a unique MLE, inherently satisfying the linearity requirement. To showcase the practical utility of replacing BTM with our EBM in the context of offline alignment, we adapt a simple yet scalable objective function from the recent literature on fitting EBM and name it as Energy Preference Alignment (EPA). Empirically, we demonstrate that EPA consistently delivers better performance on open benchmarks compared to DPO, thereby validating the theoretical superiority of our EBM.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-hong25i, title = {Energy-Based Preference Model Offers Better Offline Alignment than the Bradley-Terry Preference Model}, author = {Hong, Yuzhong and Zhang, Hanshan and Bao, Junwei and Jiang, Hongfei and Song, Yang}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {23787--23804}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/hong25i/hong25i.pdf}, url = {https://proceedings.mlr.press/v267/hong25i.html}, abstract = {Since the debut of DPO, it has been shown that aligning a target LLM with human preferences via the KL-constrained RLHF loss is mathematically equivalent to a special kind of reward modeling task. Concretely, the task requires: 1) using the target LLM to parameterize the reward model, and 2) tuning the reward model so that it has a 1:1 linear relationship with the true reward. However, we identify a significant issue: the DPO loss might have multiple minimizers, of which only one satisfies the required linearity condition. The problem arises from a well-known issue of the underlying Bradley-Terry preference model: it does not always have a unique maximum likelihood estimator (MLE). Consequently, the minimizer of the RLHF loss might be unattainable because it is merely one among many minimizers of the DPO loss. As a better alternative, we propose an energy-based preference model (EBM) that always has a unique MLE, inherently satisfying the linearity requirement. To showcase the practical utility of replacing BTM with our EBM in the context of offline alignment, we adapt a simple yet scalable objective function from the recent literature on fitting EBM and name it as Energy Preference Alignment (EPA). Empirically, we demonstrate that EPA consistently delivers better performance on open benchmarks compared to DPO, thereby validating the theoretical superiority of our EBM.} }
Endnote
%0 Conference Paper %T Energy-Based Preference Model Offers Better Offline Alignment than the Bradley-Terry Preference Model %A Yuzhong Hong %A Hanshan Zhang %A Junwei Bao %A Hongfei Jiang %A Yang Song %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-hong25i %I PMLR %P 23787--23804 %U https://proceedings.mlr.press/v267/hong25i.html %V 267 %X Since the debut of DPO, it has been shown that aligning a target LLM with human preferences via the KL-constrained RLHF loss is mathematically equivalent to a special kind of reward modeling task. Concretely, the task requires: 1) using the target LLM to parameterize the reward model, and 2) tuning the reward model so that it has a 1:1 linear relationship with the true reward. However, we identify a significant issue: the DPO loss might have multiple minimizers, of which only one satisfies the required linearity condition. The problem arises from a well-known issue of the underlying Bradley-Terry preference model: it does not always have a unique maximum likelihood estimator (MLE). Consequently, the minimizer of the RLHF loss might be unattainable because it is merely one among many minimizers of the DPO loss. As a better alternative, we propose an energy-based preference model (EBM) that always has a unique MLE, inherently satisfying the linearity requirement. To showcase the practical utility of replacing BTM with our EBM in the context of offline alignment, we adapt a simple yet scalable objective function from the recent literature on fitting EBM and name it as Energy Preference Alignment (EPA). Empirically, we demonstrate that EPA consistently delivers better performance on open benchmarks compared to DPO, thereby validating the theoretical superiority of our EBM.
APA
Hong, Y., Zhang, H., Bao, J., Jiang, H. & Song, Y.. (2025). Energy-Based Preference Model Offers Better Offline Alignment than the Bradley-Terry Preference Model. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:23787-23804 Available from https://proceedings.mlr.press/v267/hong25i.html.

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