# Probabilistic Uncertain Reward Model

arXiv: https://arxiv.org/abs/2503.22480 · HTML: https://mlsanity.com/paper/2503.22480/

## Key facts

- Cited by 1 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 17 of its 27 references that are in the map.
- First posted on arXiv 28 Mar 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, 17 of 17)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [AlpacaFarm: A Simulation Framework for Methods that Learn from Human Feedback](https://mlsanity.com/paper/2305.14387/) (2023)
- [Safe RLHF: Safe Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2310.12773/) (2023)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Monitoring Reasoning Models for Misbehavior and the Risks of Promoting Obfuscation](https://mlsanity.com/paper/2503.11926/) (2025)
- [HelpSteer2: Open-source dataset for training top-performing reward models](https://mlsanity.com/paper/2406.08673/) (2024)
- [Helping or Herding? Reward Model Ensembles Mitigate but do not Eliminate Reward Hacking](https://mlsanity.com/paper/2312.09244/) (2023)
- [ODIN: Disentangled Reward Mitigates Hacking in RLHF](https://mlsanity.com/paper/2402.07319/) (2024)
- [Reward Shaping to Mitigate Reward Hacking in RLHF](https://mlsanity.com/paper/2502.18770/) (2025)
- [Uncertainty-aware Reward Model: Teaching Reward Models to Know What is Unknown](https://mlsanity.com/paper/2410.00847/) (2024)
- [Self-Generated Critiques Boost Reward Modeling for Language Models](https://mlsanity.com/paper/2411.16646/) (2024)
- [Reward-Robust RLHF in LLMs](https://mlsanity.com/paper/2409.15360/) (2024)

## Built on by (most cited first, 1 of 1)

- [Review of Hallucination Understanding in Large Language and Vision Models](https://mlsanity.com/paper/2510.00034/) (2025)

## Abstract (arXiv)

Reinforcement learning from human feedback (RLHF) is a critical technique for training large language models. However, conventional reward models based on the Bradley-Terry model (BTRM) often suffer from overconfidence when faced with inconsistent labels or out-of-distribution samples, leading to reward hacking, where the policy model blindly optimizes for proxy rewards while degrading true performance. This paper proposes the Probabilistic Uncertain Reward Model (PURM), which generalizes the Bradley-Terry model to learn the reward distributions that emerged from the preference data. We theoretically derive the loss function of PURM and introduce a novel method that uses the overlap between distributions to quantify uncertainty. Empirical results show that PURM outperforms existing methods with more accurate reward and sound uncertainty estimations, and sustains effective learning for more optimization steps and obtain higher maximum win rate in RLHF. The data and code of this paper are released at https://anonymous.4open.science/r/Probabilistic-Uncertain-Reward-Model/