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

TL;DR

This paper provides the first theoretical analysis of the convergence properties of the LLM optimizer framework for black-box network management, supported by numerical simulations.

Contribution

It establishes a theoretical foundation for LLM-based optimization, interpreting the process as a finite-state Markov chain and analyzing convergence, including multi-LLM architectures.

Findings

Proves convergence of the LLMO framework.

Extends analysis to multiple LLMs with verified convergence rate.

Numerical simulations validate theoretical results.

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.