{"ID":2898793,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.02689","arxiv_id":"2507.02689","title":"On the Convergence of Large Language Model Optimizer for Black-Box Network Management","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.","short_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 sol...","url_abs":"https://arxiv.org/abs/2507.02689","url_pdf":"https://arxiv.org/pdf/2507.02689v1","authors":"[\"Hoon Lee\",\"Wentao Zhou\",\"Merouane Debbah\",\"Inkyu Lee\"]","published":"2025-07-03T14:59:42Z","proceeding":"cs.IT","tasks":"[\"cs.IT\",\"eess.SP\"]","methods":"[\"Large Language Model\",\"Language Model\"]","has_code":false}