Reward modeling is crucial for aligning large language models with human preferences, yet current approaches lack a principled mathematical framework for leveraging ordinal preference data. When human annotators provide graded preferences on a Likert scale (e.g., significantly better, better, slightly better, negligibly better), existing methods typically apply ad-hoc heuristics, such as margin terms or scaling factors, to loss functions derived from binary preference models like Bradley-Terry. These approaches lack an underlying mathematical model for how ordinal preference data is generated. We present a theoretically grounded framework that formulates reward modeling with Likert scale preferences as a discrete ordinal regression problem. We derive two loss functions from this formulation: a negative log-likelihood loss and an all-threshold loss, both of which learn threshold parameters that naturally capture the ordinal structure of preferences. Unlike existing heuristic methods that manually specify fixed margins or scaling weights, our approach learns these parameters directly from data within a coherent probabilistic framework. Experimental results on multiple benchmarks demonstrate that our ordinal regression approach consistently achieves competitive or superior performance compared to existing heuristic methods across diverse evaluation categories including chat, reasoning, and safety tasks. Our work provides the first principled mathematical framework for incorporating Likert scale preferences into reward model training, moving beyond ad-hoc modifications of binary preference models to enable more effective utilization of fine-grained human feedback.
Mitigating Hallucination Through Theory-Consistent Symmetric Multimodal Preference Optimization
Shandong University（山东大学）；Southern University of Science and Technology（南方科技大学）；University of Georgia（佐治亚大学）；National University of Singapore（新加坡国立大学）；Harbin Institute of Technology (Shenzhen)（哈尔滨工业大学（深圳））
Microsoft Research Asia（微软亚洲研究院）；Tsinghua University（清华大学）
Ordinal regression with anchored reference samples (ORARS) has been proposed for predicting the subjective Mean Opinion Score (MOS) of input stimuli automatically. The ORARS addresses the MOS prediction problem by pairing a test sample with each of the pre-scored anchored reference samples. A trained binary classifier is then used to predict which sample, test or anchor, is better statistically. Posteriors of the binary preference decision are then used to predict the MOS of the test sample. In this paper, rigorous framework, analysis, and experiments to demonstrate that ORARS are advantageous…
Difficulty-Based Preference Data Selection by DPO Implicit Reward Gap
Paul G. Allen School of Computer Science & Engineering, University of Washington（华盛顿大学计算机科学与工程保罗·G·艾伦学校）；Max Planck Institute for Intelligent Systems, Tübingen, Germany（德国图宾根马克斯·普朗克智能系统研究所）；Jinesis Lab, University of Toronto & Vector Institute（多伦多大学Jinesis实验室及向量研究所）
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；University of Pennsylvania（宾夕法尼亚大学）
In applications such as recommendation systems and revenue management, it is important to predict preferences on items that have not been seen by a user or predict outcomes of comparisons among those that have never been compared. A popular discrete choice model of multinomial logit model captures the structure of the hidden preferences with a low-rank matrix. In order to predict the preferences, we want to learn the underlying model from noisy observations of the low-rank matrix, collected as revealed preferences in various forms of ordinal data. A natural approach to learn such a model is to…
Collaborative filtering is an effective recommendation technique wherein the preference of an individual can potentially be predicted based on preferences of other members. Early algorithms often relied on the strong locality in the preference data, that is, it is enough to predict preference of a user on a particular item based on a small subset of other users with similar tastes or of other items with similar properties. More recently, dimensionality reduction techniques have proved to be equally competitive, and these are based on the co-occurrence patterns rather than locality. This paper …
This study presents an Ordinal version of Residual Logit (Ordinal-ResLogit) model to investigate the ordinal responses. We integrate the standard ResLogit model into COnsistent RAnk Logits (CORAL) framework, classified as a binary classification algorithm, to develop a fully interpretable deep learning-based ordinal regression model. As the formulation of the Ordinal-ResLogit model enjoys the Residual Neural Networks concept, our proposed model addresses the main constraint of machine learning algorithms, known as black-box. Moreover, the Ordinal-ResLogit model, as a binary classification fram…
Institute of Digital Games, University of Malta（马耳他大学数字游戏研究所）
Preference learning (PL) is a core area of machine learning that handles datasets with ordinal relations. As the number of generated data of ordinal nature is increasing, the importance and role of the PL field becomes central within machine learning research and practice. This paper introduces an open source, scalable, efficient and accessible preference learning toolbox that supports the key phases of the data training process incorporating various popular data preprocessing, feature selection and preference learning methods.
Ordinal data is omnipresent in almost all multiuser-generated feedback - questionnaires, preferences etc. This paper investigates modelling of ordinal data with Gaussian restricted Boltzmann machines (RBMs). In particular, we present the model architecture, learning and inference procedures for both vector-variate and matrix-variate ordinal data. We show that our model is able to capture latent opinion profile of citizens around the world, and is competitive against state-of-art collaborative filtering techniques on large-scale public datasets. The model thus has the potential to extend applic…
We present a new method for identifying the latent categorization of items based on their rankings. Complimenting a recent work that uses a Dirichlet prior on preference vectors and variational inference, we show that this problem can be effectively dealt with using existing community detection algorithms, with the communities corresponding to item categories. In particular we convert the bipartite ranking data to a unipartite graph of item affinities, and apply community detection algorithms. In this context we modify an existing algorithm - namely the label propagation algorithm to a variant…
Active Human Feedback Collection via Neural Contextual Dueling Bandits
Singapore-MIT Alliance for Research and Technology（新加坡-麻省理工联合研究技术联盟）；Department of Computer Science, National University of Singapore（国立新加坡大学计算机科学系）；The Chinese University of Hong Kong, Shenzhen, China（香港中文大学（深圳））；CSAIL, MIT, USA（MIT计算机科学与人工智能实验室）
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Rank aggregation systems collect ordinal preferences from individuals to produce a global ranking that represents the social preference. Rank-breaking is a common practice to reduce the computational complexity of learning the global ranking. The individual preferences are broken into pairwise comparisons and applied to efficient algorithms tailored for independent paired comparisons. However, due to the ignored dependencies in the data, naive rank-breaking approaches can result in inconsistent estimates. The key idea to produce accurate and consistent estimates is to treat the pairwise compar…
Data in the form of pairwise comparisons arises in many domains, including preference elicitation, sporting competitions, and peer grading among others. We consider parametric ordinal models for such pairwise comparison data involving a latent vector $w^* \in \mathbb{R}^d$ that represents the "qualities" of the $d$ items being compared; this class of models includes the two most widely used parametric models--the Bradley-Terry-Luce (BTL) and the Thurstone models. Working within a standard minimax framework, we provide tight upper and lower bounds on the optimal error in estimating the quality …
