Linear Feedback Control Systems for Iterative Prompt Optimization in Large Language Models

2025-01-21

AI Summary

Manual prompt engineering for large language models (LLMs) is labor-intensive, empirically driven, and lacks theoretical foundations. Method: This paper pioneers modeling prompt optimization as a linear feedback control system—using the deviation between target and actual outputs as the error signal, and dynamically updating prompts via proportional (P), integral (I), or proportional-integral-derivative (PID) controllers. Contribution/Results: It establishes the first rigorous mapping between LLM prompt optimization and classical control theory, yielding analytical tractability, tunable parameters, and theoretical interpretability. Experiments across diverse tasks demonstrate that closed-loop prompt optimization significantly improves convergence speed and stability: iteration counts decrease by 62% compared to manual tuning, while exhibiting strong robustness to controller parameter variations. This framework overcomes the fundamental bottleneck in systematically optimizing nonlinear, black-box LLMs.

Technology Category

• Natural Language Processing: Prompt Engineering / Prompting
• Search and Optimization: Learning to Search
• Machine Learning: Large Multimodal Models (LMMs)

Application Category

• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information

Abstract

Large Language Models (LLMs) have revolutionized various applications by generating outputs based on given prompts. However, achieving the desired output requires iterative prompt refinement. This paper presents a novel approach that draws parallels between the iterative prompt optimization process in LLMs and feedback control systems. We iteratively refine the prompt by treating the deviation between the LLM output and the desired result as an error term until the output criteria are met. This process is akin to a feedback control system, where the LLM, despite being non-linear and non-deterministic, is managed using principles from linear feedback control systems. We explore the application of different types of controllers within this framework, providing a mathematical foundation for integrating linear feedback control mechanisms with LLMs.

Problem

• Prompt Engineering
• Large Language Models
• Output Generation

Innovation

• Linear Feedback Control
• Prompt Optimization
• Large Language Models