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

Hoon Lee; Wentao Zhou; Merouane Debbah; Inkyu Lee

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arXiv · 2507.02689

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

Hoon Lee·Wentao Zhou·Merouane Debbah·Inkyu Lee

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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.

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Hoon Lee, Wentao Zhou, Merouane Debbah, Inkyu Lee. 2025-07-03. On the Convergence of Large Language Model Optimizer for Black-Box Network Management. https://arxiv.org/abs/2507.02689

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