Why Self-Rewarding Works: Theoretical Guarantees for Iterative Alignment of Language Models

2026-01-30

AI Summary

Self-Rewarding Language Models (SRLMs) can iteratively improve alignment without external feedback, yet their theoretical underpinnings remain unclear. This work provides the first rigorous theoretical guarantees for SRLMs by establishing a statistical learning framework grounded in finite-sample analysis. We derive a lower bound for single-step updates and an error bound characterizing the full iterative process, instantiated through a linear softmax model. Our analysis proves that model performance converges at a rate of $\widetilde{\mathcal{O}}(1/\sqrt{n})$ with respect to sample size $n$, while the influence of the initial model decays exponentially with the number of iterations. These results elucidate the core mechanism by which multi-round self-rewarding overcomes poor initialization, ultimately achieving internal consistency and stability.

Technology Category

• Machine Learning: Learning Theory
• Natural Language Processing: (Large) Language Models
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Self-Rewarding Language Models (SRLMs) achieve notable success in iteratively improving alignment without external feedback. Yet, despite their striking empirical progress, the core mechanisms driving their capabilities remain unelucidated, leaving a critical gap in theoretical understanding. This paper provides the first rigorous theoretical guarantees for SRLMs. We first establish a lower bound that characterizes the fundamental limits of a single update step, revealing a critical dependence on the quality of the initial model. We then derive finite-sample error bounds for the full iterative paradigm, showing that performance improves at a rate of $\widetilde{\mathcal{O}}\left(1/\sqrt{n}\right)$ with sample size $n$. Crucially, our analysis reveals that the dependence on the initial model decays exponentially with the number of iterations $T$. This provides a formal explanation for why self-rewarding succeeds: it robustly overcomes poor initialization by steering the dynamics toward internal stability and consistency. Finally, we instantiate our theoretical framework for the linear softmax model class, yielding tailored guarantees that connect our high-level insights to practical model architectures.

Problem

• Self-Rewarding Language Models
• iterative alignment
• theoretical guarantees
• model initialization
• language model alignment

Innovation

• Self-Rewarding Language Models
• Theoretical Guarantees
• Iterative Alignment
• Finite-Sample Error Bounds
• Exponential Decay of Initialization Dependence