# KL-Regularized RLHF with Multiple Reference Models: Exact Solutions and Sample Complexity

arXiv: https://arxiv.org/abs/2502.01203 · HTML: https://mlsanity.com/paper/2502.01203/

## 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 31 of its 44 references that are in the map.
- First posted on arXiv 3 Feb 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 31)

- [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)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [RealToxicityPrompts: Evaluating Neural Toxic Degeneration in Language Models](https://mlsanity.com/paper/2009.11462/) (2020)
- [The RefinedWeb Dataset for Falcon LLM: Outperforming Curated Corpora with Web Data, and Web Data Only](https://mlsanity.com/paper/2306.01116/) (2023)
- [Iterative Preference Learning from Human Feedback: Bridging Theory and Practice for RLHF under KL-Constraint](https://mlsanity.com/paper/2312.11456/) (2023)
- [Skywork-Reward: Bag of Tricks for Reward Modeling in LLMs](https://mlsanity.com/paper/2410.18451/) (2024)
- [Beyond Reverse KL: Generalizing Direct Preference Optimization with Diverse Divergence Constraints](https://mlsanity.com/paper/2309.16240/) (2023)
- [Pessimistic Model-based Offline Reinforcement Learning under Partial Coverage](https://mlsanity.com/paper/2107.06226/) (2021)
- [Theoretical guarantees on the best-of-n alignment policy](https://mlsanity.com/paper/2401.01879/) (2024)
- [Offline Reinforcement Learning with Realizability and Single-policy Concentrability](https://mlsanity.com/paper/2202.04634/) (2022)
- [Correcting the Mythos of KL-Regularization: Direct Alignment without Overoptimization via Chi-Squared Preference Optimization](https://mlsanity.com/paper/2407.13399/) (2024)
- [Provable Offline Preference-Based Reinforcement Learning](https://mlsanity.com/paper/2305.14816/) (2023)
- [The Importance of Online Data: Understanding Preference Fine-tuning via Coverage](https://mlsanity.com/paper/2406.01462/) (2024)
- [Dataset Reset Policy Optimization for RLHF](https://mlsanity.com/paper/2404.08495/) (2024)
- [InfAlign: Inference-aware language model alignment](https://mlsanity.com/paper/2412.19792/) (2024)
- [Sharp Analysis for KL-Regularized Contextual Bandits and RLHF](https://mlsanity.com/paper/2411.04625/) (2024)
- [Inverse-RLignment: Large Language Model Alignment from Demonstrations through Inverse Reinforcement Learning](https://mlsanity.com/paper/2405.15624/) (2024)
- [Information Theoretic Guarantees For Policy Alignment In Large Language Models](https://mlsanity.com/paper/2406.05883/) (2024)
- [Multi-Reference Preference Optimization for Large Language Models](https://mlsanity.com/paper/2405.16388/) (2024)
- [Soft Preference Optimization: Aligning Language Models to Expert Distributions](https://mlsanity.com/paper/2405.00747/) (2024)
- [Learning to Constrain Policy Optimization with Virtual Trust Region](https://mlsanity.com/paper/2204.09315/) (2022)
- [SALSA: Soup-based Alignment Learning for Stronger Adaptation in RLHF](https://mlsanity.com/paper/2411.01798/) (2024)

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

- [Reinforcement Learning with Verifiable Rewards: GRPO's Effective Loss, Dynamics, and Success Amplification](https://mlsanity.com/paper/2503.06639/) (2025)
- [What Makes a Reward Model a Good Teacher? An Optimization Perspective](https://mlsanity.com/paper/2503.15477/) (2025)
- [Demystifying Group Relative Policy Optimization: Its Policy Gradient is a U-Statistic](https://mlsanity.com/paper/2603.01162/) (2026)
- [SafeMobile: Chain-level Jailbreak Detection and Automated Evaluation for Multimodal Mobile Agents](https://mlsanity.com/paper/2507.00841/) (2025)
- [Robust Reinforcement Learning from Human Feedback for Large Language Models Fine-Tuning](https://mlsanity.com/paper/2504.03784/) (2025)
- [Provably Efficient Regularized Online RLHF with Generalized Bilinear Preferences](https://mlsanity.com/paper/2602.23116/) (2026)
- [Offline and Online KL-Regularized RLHF under Differential Privacy](https://mlsanity.com/paper/2510.13512/) (2025)
- [Theoretical Perspectives on Data Quality and Synergistic Effects in Pre- and Post-Training Reasoning Models](https://mlsanity.com/paper/2603.01293/) (2026)
- [Privacy-Preserving Reinforcement Learning from Human Feedback via Decoupled Reward Modeling](https://mlsanity.com/paper/2603.22563/) (2026)
- [Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability](https://mlsanity.com/paper/2605.09214/) (2026)
- [f-Divergence Regularized RLHF: Two Tales of Sampling and Unified Analyses](https://mlsanity.com/paper/2605.06977/) (2026)

## Abstract (arXiv)

Recent methods for aligning large language models (LLMs) with human feedback predominantly rely on a single reference model, which limits diversity, model overfitting, and underutilizes the wide range of available pre-trained models. Incorporating multiple reference models has the potential to address these limitations by broadening perspectives, reducing bias, and leveraging the strengths of diverse open-source LLMs. However, integrating multiple reference models into reinforcement learning with human feedback (RLHF) frameworks poses significant theoretical challenges, where achieving exact solutions has remained an open problem. This paper presents the first exact solution to the multiple reference model problem in reverse KL-regularized RLHF. We introduce a comprehensive theoretical framework that includes rigorous statistical analysis and provides sample complexity guarantees. Additionally, we extend our analysis to forward KL-regularized RLHF, offering new insights into sample complexity requirements in multiple reference scenarios. Our contributions lay the foundation for more advanced and adaptable LLM alignment techniques, enabling the effective use of multiple reference models. This work paves the way for developing alignment frameworks that are both theoretically sound and better suited to the challenges of modern AI ecosystems.