Rethinking Reward Modeling in Preference-based Large Language Model Alignment
Hao Sun Yunyi Shen Jean-Francois Ton
The Bradley-Terry (BT) model is a common and successful practice in reward modeling for Large Language Model (LLM) alignment. However, it remains unclear *why* this model --- originally developed for multi-player stochastic game matching --- can be adopted to convert pairwise response comparisons to reward values and make predictions. Especially given the fact that only a limited number of prompt-response pairs are sparsely compared with others. 
In this paper, we first establish the convergence rate of BT reward models based on deep neural networks using embeddings, providing a theoretical foundation for their use.
Despite theoretically sound, we argue that the BT model is not a necessary choice from the perspective of downstream optimization, this is because a reward model only needs to preserve the correct ranking predictions through a monotonic transformation of the true reward. 
We highlight the critical concept of *order consistency* in reward modeling and demonstrate that the BT model possesses this property.
Moreover, we propose a simple and straightforward upper-bound algorithm, compatible with off-the-shelf binary classifiers, as an alternative order-consistent reward modeling objective. 
To offer practical insights, we empirically evaluate the performance of these different reward modeling approaches across more than 12,000 experimental setups, using $6$ base LLMs, $2$ datasets, and diverse annotation designs that vary in quantity, quality, and pairing choices in preference annotations.
Bradley-Terry Model, Reward Modeling, Large Language Models