How Sampling Shapes LLM Alignment: From One-Shot Optima to Iterative Dynamics

2026-02-12

AI Summary

This work addresses the lack of theoretical grounding in the choice of sampling and reference strategies for preference alignment in large language models, which often leads to training instability or performance degradation. The study provides the first theoretical characterization of the benefits and risks of instance-dependent sampling, integrating Identity Preference Optimization and Direct Preference Optimization frameworks to analyze both single-step optimality and iterative dynamics. It reveals that sampling bias can induce entropy collapse and persistent oscillations during training. Building on theoretical analysis and empirical validation with real-world preference data, the paper establishes stability conditions that guarantee convergence and demonstrates that well-designed sampling strategies substantially improve ranking performance and alignment robustness.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Knowledge Representation and Reasoning: Preferences
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Standard methods for aligning large language models with human preferences learn from pairwise comparisons among sampled candidate responses and regularize toward a reference policy. Despite their effectiveness, the effects of sampling and reference choices are poorly understood theoretically. We investigate these effects through Identity Preference Optimization, a widely used preference alignment framework, and show that proper instance-dependent sampling can yield stronger ranking guarantees, while skewed on-policy sampling can induce excessive concentration under structured preferences. We then analyze iterative alignment dynamics in which the learned policy feeds back into future sampling and reference policies, reflecting a common practice of model-generated preference data. We prove that these dynamics can exhibit persistent oscillations or entropy collapse for certain parameter choices, and characterize regimes that guarantee stability. Our theoretical insights extend to Direct Preference Optimization, indicating the phenomena we captured are common to a broader class of preference-alignment methods. Experiments on real-world preference data validate our findings.

Problem

• sampling
• LLM alignment
• preference optimization
• iterative dynamics
• reference policy

Innovation

• sampling dynamics
• preference alignment
• iterative optimization
• entropy collapse
• stability analysis