On the Convergence of Large Language Model Optimizer for Black-Box Network Management

2025-07-03

AI Summary

To address black-box wireless network management—where no universal mathematical model exists—this paper establishes the first rigorous theoretical foundation for large language model (LLM)-based optimizers. We propose an LLM-as-optimizer framework wherein a pre-trained LLM serves as the optimization agent, iteratively generating strategies via natural-language prompting and historical solution feedback. The optimization process is formally modeled as a finite-state Markov chain, enabling the first convergence analysis framework for LLM-driven optimization; this framework is further extended to multi-LLM collaborative architectures. We theoretically prove global convergence of the LLM optimizer and empirically validate that multi-LLM coordination significantly accelerates convergence. This work bridges a critical theoretical gap in applying LLMs to black-box network optimization, uncovers their underlying optimization mechanisms, and introduces an interpretable, analyzable paradigm for LLM-powered intelligent network management.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Optimization
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• 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
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Future wireless networks are expected to incorporate diverse services that often lack general mathematical models. To address such black-box network management tasks, the large language model (LLM) optimizer framework, which leverages pretrained LLMs as optimization agents, has recently been promoted as a promising solution. This framework utilizes natural language prompts describing the given optimization problems along with past solutions generated by LLMs themselves. As a result, LLMs can obtain efficient solutions autonomously without knowing the mathematical models of the objective functions. Although the viability of the LLM optimizer (LLMO) framework has been studied in various black-box scenarios, it has so far been limited to numerical simulations. For the first time, this paper establishes a theoretical foundation for the LLMO framework. With careful investigations of LLM inference steps, we can interpret the LLMO procedure as a finite-state Markov chain, and prove the convergence of the framework. Our results are extended to a more advanced multiple LLM architecture, where the impact of multiple LLMs is rigorously verified in terms of the convergence rate. Comprehensive numerical simulations validate our theoretical results and provide a deeper understanding of the underlying mechanisms of the LLMO framework.

Problem

• Theoretical foundation for LLM optimizer in black-box networks
• Convergence proof of LLM optimizer as Markov chain
• Impact of multiple LLMs on convergence rate

Innovation

• Leverages pretrained LLMs as optimization agents
• Uses natural language prompts for problem description
• Interprets LLMO as finite-state Markov chain