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Reward learning plays a pivotal role in Reinforcement Learning from Human Feedback (RLHF), ensuring the alignment of language models. The Bradley-Terry (BT) model stands as the prevalent choice for capturing human preferences from datasets…

Machine Learning · Computer Science 2024-10-10 Jinsong Liu , Dongdong Ge , Ruihao Zhu

Many properties in the real world don't have metrics and can't be numerically observed, making them difficult to learn. To deal with this challenging problem, prior works have primarily focused on estimating those properties by using graded…

Machine Learning · Computer Science 2024-03-12 Satoru Fujii

The rating of items based on pairwise comparisons has been a topic of statistical investigation for many decades. Numerous approaches have been proposed. One of the best known is the Bradley-Terry model. This paper seeks to assemble and…

Statistics Theory · Mathematics 2025-08-08 Ian Hamilton , Nick Tawn , David Firth

Pairwise preference learning is central to machine learning, with recent applications in aligning language models with human preferences. A typical dataset consists of triplets $(x, y^+, y^-)$, where response $y^+$ is preferred over…

Machine Learning · Computer Science 2026-02-12 Rattana Pukdee , Maria-Florina Balcan , Pradeep Ravikumar

This paper introduces the Bradley-Terry Regression Trunk model, a novel probabilistic approach for the analysis of preference data expressed through paired comparison rankings. In some cases, it may be reasonable to assume that the…

The Bradley-Terry model assigns probabilities for the outcome of paired comparison experiments based on strength parameters associated with the objects being compared. We consider different proposed choices of prior parameter distributions…

Statistics Theory · Mathematics 2017-12-15 John T. Whelan

Several methods of preference modeling, ranking, voting and multi-criteria decision making include pairwise comparisons. It is usually simpler to compare two objects at a time, furthermore, some relations (e.g., the outcome of sports…

Optimization and Control · Mathematics 2025-09-04 László Gyarmati , Éva Orbán-Mihálykó , Csaba Mihálykó , Sándor Bozóki , Zsombor Szádoczki

Pairwise comparison data are widely used to infer latent rankings in areas such as sports, social choice, and machine learning. The Bradley-Terry model provides a foundational probabilistic framework but inherently assumes transitive…

Methodology · Statistics 2026-01-13 Hisaya Okahara , Tomoyuki Nakagawa , Shonosuke Sugasawa

We study the ranking of individuals, teams, or objects, based on pairwise comparisons between them, using the Bradley-Terry model. Estimates of rankings within this model are commonly made using a simple iterative algorithm first introduced…

Machine Learning · Statistics 2023-08-16 M. E. J. Newman

This paper presents a novel technique for incorporating user input when learning and inferring user preferences. When trying to provide users of black-box machine learning models with actionable recourse, we often wish to incorporate their…

Machine Learning · Computer Science 2024-09-24 Kaivalya Rawal , Himabindu Lakkaraju

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 --…

Artificial Intelligence · Computer Science 2025-01-28 Hao Sun , Yunyi Shen , Jean-Francois Ton

This paper studies human preference learning based on partially revealed choice behavior and formulates the problem as a generalized Bradley-Terry-Luce (BTL) ranking model that accounts for heterogeneous preferences. Specifically, we assume…

Methodology · Statistics 2025-09-03 Jianqing Fan , Hyukjun Kwon , Xiaonan Zhu

Ranking items based on pairwise comparisons is common, from using match outcomes to rank sports teams to using purchase or survey data to rank consumer products. Statistical inference-based methods such as the Bradley-Terry model, which…

Physics and Society · Physics 2026-01-09 Sebastian Morel-Balbi , Alec Kirkley

Real-life combinatorial optimization problems often involve several conflicting objectives, such as price, product quality and sustainability. A computationally-efficient way to tackle multiple objectives is to aggregate them into a…

Artificial Intelligence · Computer Science 2025-08-28 Marianne Defresne , Jayanta Mandi , Tias Guns

Transfer learning is a widely used method to build high performing computer vision models. In this paper, we study the efficacy of transfer learning by examining how the choice of data impacts performance. We find that more pre-training…

Computer Vision and Pattern Recognition · Computer Science 2018-12-13 Jiquan Ngiam , Daiyi Peng , Vijay Vasudevan , Simon Kornblith , Quoc V. Le , Ruoming Pang

Transfer learning has recently attracted significant research attention, as it simultaneously learns from different source domains, which have plenty of labeled data, and transfers the relevant knowledge to the target domain with limited…

Machine Learning · Statistics 2018-06-14 Alireza Karbalayghareh , Xiaoning Qian , Edward R. Dougherty

We propose a novel adaptive transfer learning framework, learning to transfer learn (L2TL), to improve performance on a target dataset by careful extraction of the related information from a source dataset. Our framework considers…

Machine Learning · Computer Science 2020-07-17 Linchao Zhu , Sercan O. Arik , Yi Yang , Tomas Pfister

Evaluating the pedagogical quality of AI tutors remains challenging: standard NLG metrics do not determine whether responses identify mistakes, scaffold reasoning, or avoid revealing the answers. For the task of mistake remediation, we…

Computation and Language · Computer Science 2026-03-26 Kseniia Petukhova , Ekaterina Kochmar

Molecules have a number of distinct properties whose importance and application vary. Often, in reality, labels for some properties are hard to achieve despite their practical importance. A common solution to such data scarcity is to use…

Machine Learning · Computer Science 2024-10-02 Chanhui Lee , Dae-Woong Jeong , Sung Moon Ko , Sumin Lee , Hyunseung Kim , Soorin Yim , Sehui Han , Sungwoong Kim , Sungbin Lim

This paper is dedicated to a cautious learning methodology for predicting preferences between alternatives characterized by binary attributes (formally, each alternative is seen as a subset of attributes). By "cautious", we mean that the…

Artificial Intelligence · Computer Science 2022-06-16 Hugo Gilbert , Mohamed Ouaguenouni , Meltem Ozturk , Olivier Spanjaard
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