# Towards a Theoretical Understanding to the Generalization of RLHF

arXiv: https://arxiv.org/abs/2601.16403 · HTML: https://mlsanity.com/paper/2601.16403/

## Key facts

- Cited by 6 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 44 of its 53 references that are in the map.
- First posted on arXiv 23 Jan 2026.

## 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 44)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [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)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/1608.04636/) (2016)
- [VLM-R1: A Stable and Generalizable R1-style Large Vision-Language Model](https://mlsanity.com/paper/2504.07615/) (2025)
- [Provably Efficient Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/1907.05388/) (2019)
- [Sora: A Review on Background, Technology, Limitations, and Opportunities of Large Vision Models](https://mlsanity.com/paper/2402.17177/) (2024)
- [Iterative Preference Learning from Human Feedback: Bridging Theory and Practice for RLHF under KL-Constraint](https://mlsanity.com/paper/2312.11456/) (2023)
- [π*0.6: a VLA That Learns From Experience](https://mlsanity.com/paper/2511.14759/) (2025)
- [Is DPO Superior to PPO for LLM Alignment? A Comprehensive Study](https://mlsanity.com/paper/2404.10719/) (2024)
- [Principled Reinforcement Learning with Human Feedback from Pairwise or K-wise Comparisons](https://mlsanity.com/paper/2301.11270/) (2023)
- [A Theoretical Analysis of Deep Q-Learning](https://mlsanity.com/paper/1901.00137/) (2019)
- [Stability of Stochastic Gradient Descent on Nonsmooth Convex Losses](https://mlsanity.com/paper/2006.06914/) (2020)
- [Fine-Grained Analysis of Stability and Generalization for Stochastic Gradient Descent](https://mlsanity.com/paper/2006.08157/) (2020)
- [Dueling RL: Reinforcement Learning with Trajectory Preferences](https://mlsanity.com/paper/2111.04850/) (2021)
- [Preference-based Online Learning with Dueling Bandits: A Survey](https://mlsanity.com/paper/1807.11398/) (2018)
- [Contextual Dueling Bandits](https://mlsanity.com/paper/1502.06362/) (2015)
- [High probability generalization bounds for uniformly stable algorithms with nearly optimal rate](https://mlsanity.com/paper/1902.10710/) (2019)
- [Tight Analyses for Non-Smooth Stochastic Gradient Descent](https://mlsanity.com/paper/1812.05217/) (2018)
- [Sharper bounds for uniformly stable algorithms](https://mlsanity.com/paper/1910.07833/) (2019)
- [Data-Dependent Stability of Stochastic Gradient Descent](https://mlsanity.com/paper/1703.01678/) (2017)

## Built on by (most cited first, 6 of 6)

- [Maximum Likelihood Reinforcement Learning](https://mlsanity.com/paper/2602.02710/) (2026)
- [Reasoning and Tool-use Compete in Agentic RL:From Quantifying Interference to Disentangled Tuning](https://mlsanity.com/paper/2602.00994/) (2026)
- [ETS: Energy-Guided Test-Time Scaling for Training-Free RL Alignment](https://mlsanity.com/paper/2601.21484/) (2026)
- [Turning Off-Policy Tokens On-Policy: A Plug-in Approach for Improving LLM Alignment](https://mlsanity.com/paper/2607.04728/) (2026)
- [Generalisation of RLHF under Reward Shift and Clipped KL Regularisation](https://mlsanity.com/paper/2602.21765/) (2026)
- [MERIT: Multimodal Evidence Reasoning over Image Tables](https://mlsanity.com/paper/2610.17937/) (2026)

## Abstract (arXiv)

Reinforcement Learning from Human Feedback (RLHF) and its variants have emerged as the dominant approaches for aligning Large Language Models with human intent. While empirically effective, the theoretical generalization properties of these methods in high-dimensional settings remain to be explored. To this end, we build the generalization theory on RLHF of LLMs under the linear reward model, through the framework of algorithmic stability. In contrast to the existing works built upon the consistency of maximum likelihood estimations on reward model, our analysis is presented under an end-to-end learning framework, which is consistent with practice. Concretely, we prove that under a key feature coverage condition, the empirical optima of policy model have a generalization bound of order O(n^-frac12). Moreover, the results can be extrapolated to parameters obtained by gradient-based learning algorithms, i.e., Gradient Ascent (GA) and Stochastic Gradient Ascent (SGA). Thus, we argue that our results provide new theoretical evidence for the empirically observed generalization of LLMs after RLHF.