Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Gholamali Aminian, Amir R. Asadi, Idan Shenfeld, Youssef Mroueh

TL;DR

The paper develops a theoretical framework for KL-regularized RLHF with multiple reference models, delivering the first exact solution for reverse KL regularization and establishing sample-complexity guarantees. It extends the analysis to forward KL regularization, deriving implicit solutions and corresponding bounds. The results show that multi-reference RLHF can achieve tighter sub-optimality gaps and favorable sample complexities compared to single-reference approaches, with practical implications for aligning LLMs using diverse open-source references. Experiments on GSM8K and UltraFeedback corroborate the theoretical advantages, highlighting improved alignment when leveraging multiple references. The work also discusses extensions to DPO and outlines important future directions like unbounded rewards and generalized divergences.

Abstract

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 \emph{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.

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

TL;DR

The paper develops a theoretical framework for KL-regularized RLHF with multiple reference models, delivering the first exact solution for reverse KL regularization and establishing sample-complexity guarantees. It extends the analysis to forward KL regularization, deriving implicit solutions and corresponding bounds. The results show that multi-reference RLHF can achieve tighter sub-optimality gaps and favorable sample complexities compared to single-reference approaches, with practical implications for aligning LLMs using diverse open-source references. Experiments on GSM8K and UltraFeedback corroborate the theoretical advantages, highlighting improved alignment when leveraging multiple references. The work also discusses extensions to DPO and outlines important future directions like unbounded rewards and generalized divergences.

Abstract

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 \emph{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.

Paper Structure

This paper contains 24 sections, 22 theorems, 97 equations, 1 figure, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Preliminaries
  4. Notations:
  5. Problem Formulation
  6. RLHF from One Reference Model
  7. Assumptions
  8. RLHF from Multiple Reference Models via Reverse KL divergence
  9. Exact Solution of RLHF under multiple reference models via RKL
  10. Main Results for RLHF via RKL
  11. RLHF from Multiple Reference Models via Forward KL Divergence
  12. Solution of RLHF under multiple reference models via FKL
  13. Main Results for RLHF with FKL
  14. Discussion
  15. Experiments
  16. ...and 9 more sections

Key Result

Theorem 5.1

Consider the following objective function for RLHF with multiple reference models, where $\sum_{i=1}^K \alpha_i=1$ and $\alpha_i\in(0,1)$ for $i\in[K]$. Then, the exact solution of the multiple reference model objective function for RLHF is, where and $\widehat{Z}(x)=\sum_{y}\widehat{\pi}_{\pmb{\alpha},\mathrm{ref}}(y|x)\exp(\gamma r_{\theta^{\star}}(x,y)).$ The maximum objective value is $\fra

Figures (1)

  • Figure 1: In both online and offline RL, our analytical RKL objective outperforms both the MRPO approximation and single reference objective ($\alpha=0$).

Theorems & Definitions (46)

  • Definition 3.1: Escort and Generalized Escort Distributions
  • Definition 3.2
  • Theorem 5.1
  • Theorem 5.2
  • Theorem 5.3
  • Remark 5.4: Sample Complexity
  • Theorem 6.1
  • Theorem 6.2
  • Theorem 6.3
  • Remark 6.4: Sample Complexity
  • ...and 36 more