# Bradley-Terry and Multi-Objective Reward Modeling Are Complementary

arXiv: https://arxiv.org/abs/2507.07375 · HTML: https://mlsanity.com/paper/2507.07375/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in Reward modeling and RLHF, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 62 of its 74 references that are in the map.
- First posted on arXiv 10 Jul 2025.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Reward modeling and RLHF](https://mlsanity.com/alignment/reward-modeling-and-rlhf/)

## Builds on (most cited first, 30 of 62)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [A Survey on Evaluation of Large Language Models](https://mlsanity.com/paper/2307.03109/) (2023)
- [Chatbot Arena: An Open Platform for Evaluating LLMs by Human Preference](https://mlsanity.com/paper/2403.04132/) (2024)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [A Survey on Large Language Models for Code Generation](https://mlsanity.com/paper/2406.00515/) (2024)
- [Safe RLHF: Safe Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2310.12773/) (2023)
- [Prometheus: Inducing Fine-grained Evaluation Capability in Language Models](https://mlsanity.com/paper/2310.08491/) (2023)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [From Generation to Judgment: Opportunities and Challenges of LLM-as-a-judge](https://mlsanity.com/paper/2411.16594/) (2024)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [Fine-Grained Human Feedback Gives Better Rewards for Language Model Training](https://mlsanity.com/paper/2306.01693/) (2023)
- [Interpretable Preferences via Multi-Objective Reward Modeling and Mixture-of-Experts](https://mlsanity.com/paper/2406.12845/) (2024)
- [Skywork-Reward: Bag of Tricks for Reward Modeling in LLMs](https://mlsanity.com/paper/2410.18451/) (2024)
- [RLHF Workflow: From Reward Modeling to Online RLHF](https://mlsanity.com/paper/2405.07863/) (2024)
- [Large Language Model Alignment: A Survey](https://mlsanity.com/paper/2309.15025/) (2023)
- [HelpSteer2: Open-source dataset for training top-performing reward models](https://mlsanity.com/paper/2406.08673/) (2024)
- [Reward Model Ensembles Help Mitigate Overoptimization](https://mlsanity.com/paper/2310.02743/) (2023)
- [Using an LLM to Help With Code Understanding](https://mlsanity.com/paper/2307.08177/) (2023)

## Built on by (most cited first, 11 of 11)

- [A Comprehensive Survey on Reinforcement Learning-based Agentic Search: Foundations, Roles, Optimizations, Evaluations, and Applications](https://mlsanity.com/paper/2510.16724/) (2025)
- [Exploring Reasoning Reward Model for Agents](https://mlsanity.com/paper/2601.22154/) (2026)
- [Unlocking the Power of Multi-Agent LLM for Reasoning: From Lazy Agents to Deliberation](https://mlsanity.com/paper/2511.02303/) (2025)
- [P-Check: Advancing Personalized Reward Model via Learning to Generate Dynamic Checklist](https://mlsanity.com/paper/2601.02986/) (2026)
- [Pragma-VL: Towards a Pragmatic Arbitration of Safety and Helpfulness in MLLMs](https://mlsanity.com/paper/2603.13292/) (2026)
- [Reward Modeling for Multi-Agent Orchestration](https://mlsanity.com/paper/2606.13598/) (2026)
- [Themis: Training Robust Multilingual Code Reward Models for Flexible Multi-Criteria Scoring](https://mlsanity.com/paper/2605.00754/) (2026)
- [From Sparse Decisions to Dense Reasoning: A Multi-attribute Trajectory Paradigm for Multimodal Moderation](https://mlsanity.com/paper/2602.02536/) (2026)
- [Variance-aware Reward Modeling with Anchor Guidance](https://mlsanity.com/paper/2605.11865/) (2026)
- [RMB: Reward Model Boosting Mitigates Reward Hacking](https://mlsanity.com/paper/2609.33221/) (2026)
- [DUALVIEW: Leveraging Broad and Output-Specific Evidence for LLM-based Multi-Output Text Regression](https://mlsanity.com/paper/2610.19206/) (2026)

## Abstract (arXiv)

Reward models trained on human preference data have demonstrated strong effectiveness in aligning Large Language Models (LLMs) with human intent under the framework of Reinforcement Learning from Human Feedback (RLHF). However, RLHF remains vulnerable to reward hacking, where the policy exploits imperfections in the reward function rather than genuinely learning the intended behavior. Although significant efforts have been made to mitigate reward hacking, they predominantly focus on and evaluate in-distribution scenarios, where the training and testing data for the reward model share the same distribution. In this paper, we empirically show that state-of-the-art methods struggle in more challenging out-of-distribution (OOD) settings. We further demonstrate that incorporating fine-grained multi-attribute scores helps address this challenge. However, the limited availability of high-quality data often leads to weak performance of multi-objective reward functions, which can negatively impact overall performance and become the bottleneck. To address this issue, we propose a unified reward modeling framework that jointly trains Bradley--Terry (BT) single-objective and multi-objective regression-based reward functions using a shared embedding space. We theoretically establish a connection between the BT loss and the regression objective and highlight their complementary benefits. Specifically, the regression task enhances the single-objective reward function's ability to mitigate reward hacking in challenging OOD settings, while BT-based training improves the scoring capability of the multi-objective reward function, enabling a 7B model to outperform a 70B baseline. Extensive experimental results demonstrate that our framework significantly improves both the robustness and the scoring performance of reward models.