# Learning Guarantee of Reward Modeling Using Deep Neural Networks

arXiv: https://arxiv.org/abs/2505.06601 · HTML: https://mlsanity.com/paper/2505.06601/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reward modeling and RLHF, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 29 of its 45 references that are in the map.
- First posted on arXiv 10 May 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, 29 of 29)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Preference Ranking Optimization for Human Alignment](https://mlsanity.com/paper/2306.17492/) (2023)
- [Principled Reinforcement Learning with Human Feedback from Pairwise or K-wise Comparisons](https://mlsanity.com/paper/2301.11270/) (2023)
- [Secrets of RLHF in Large Language Models Part II: Reward Modeling](https://mlsanity.com/paper/2401.06080/) (2024)
- [Distributional Preference Learning: Understanding and Accounting for Hidden Context in RLHF](https://mlsanity.com/paper/2312.08358/) (2023)
- [Dueling RL: Reinforcement Learning with Trajectory Preferences](https://mlsanity.com/paper/2111.04850/) (2021)
- [Gradient Descent on Two-layer Nets: Margin Maximization and Simplicity Bias](https://mlsanity.com/paper/2110.13905/) (2021)
- [Human-in-the-loop: Provably Efficient Preference-based Reinforcement Learning with General Function Approximation](https://mlsanity.com/paper/2205.11140/) (2022)
- [Estimation from Pairwise Comparisons: Sharp Minimax Bounds with Topology Dependence](https://mlsanity.com/paper/1505.01462/) (2015)
- [Provable Offline Preference-Based Reinforcement Learning](https://mlsanity.com/paper/2305.14816/) (2023)
- [Fast convergence rates of deep neural networks for classification](https://mlsanity.com/paper/1812.03599/) (2018)
- [TLCR: Token-Level Continuous Reward for Fine-grained Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2407.16574/) (2024)
- [AlignDiff: Aligning Diverse Human Preferences via Behavior-Customisable Diffusion Model](https://mlsanity.com/paper/2310.02054/) (2023)
- [Provable Pluralistic Alignment: Multi-Party RLHF under Offline Human Feedback](https://mlsanity.com/paper/2403.05006/) (2024)
- [Understanding Scaling Laws with Statistical and Approximation Theory for Transformer Neural Networks on Intrinsically Low-dimensional Data](https://mlsanity.com/paper/2411.06646/) (2024)
- [Efficient active learning of sparse halfspaces with arbitrary bounded noise](https://mlsanity.com/paper/2002.04840/) (2020)
- [Learning General Halfspaces with General Massart Noise under the Gaussian Distribution](https://mlsanity.com/paper/2108.08767/) (2021)
- [Dual Active Learning for Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2410.02504/) (2024)
- [Generalization Error Bounds for Deep Neural Networks Trained by SGD](https://mlsanity.com/paper/2206.03299/) (2022)
- [Reward Modeling with Ordinal Feedback: Wisdom of the Crowd](https://mlsanity.com/paper/2411.12843/) (2024)
- [On Extending Direct Preference Optimization to Accommodate Ties](https://mlsanity.com/paper/2409.17431/) (2024)
- [Value Enhancement of Reinforcement Learning via Efficient and Robust Trust Region Optimization](https://mlsanity.com/paper/2301.02220/) (2023)
- [Approximation Bounds for Transformer Networks with Application to Regression](https://mlsanity.com/paper/2504.12175/) (2025)

## Abstract (arXiv)

In this work, we study the learning theory of reward modeling with pairwise comparison data using deep neural networks. We establish a novel non-asymptotic regret bound for deep reward estimators in a non-parametric setting, which depends explicitly on the network architecture. Furthermore, to underscore the critical importance of clear human beliefs, we introduce a margin-type condition that assumes the conditional winning probability of the optimal action in pairwise comparisons is significantly distanced from 1/2. This condition enables a sharper regret bound, which substantiates the empirical efficiency of Reinforcement Learning from Human Feedback and highlights clear human beliefs in its success. Notably, this improvement stems from high-quality pairwise comparison data implied by the margin-type condition, is independent of the specific estimators used, and thus applies to various learning algorithms and models.