DeepSeek: Leveraging Large Language Models for Lyapunov OptimizationDesign in Telecommunications

Introduction: Lyapunov Optimization (LO) is an efficient strategy for addressing stochastic mathematical problems, yet its complexity can be daunting for academic newcomers. Limited research has explored large Language Models (LLMs) such as DeepSeek for targeted LO support. This study aims to leverage LLMs via in-context learning to simplify LO design, making it more accessible to non-expert users. Methods: This paper adopts in-context learning with a chain-of-thought prompting paradigm, leveraging LLMs to guide three core steps: problem conversion to Lyapunov standard form, long-term problem decomposition into per-slot decisions, and performance-delay trade-off analysis. Results: By examining a Wireless network power allocation case study, DeepSeek demonstrates the capability to enhance LO design by guiding constraint transformation and facilitating systematic mathematical derivation. Discussion: To further assess the value proposition, this paper evaluates responses across three dimensions: Derivation Accuracy, Workflow Completeness, and Newcomer Accessibility. DeepSeek successfully completes the full LO workflow with high correctness (only non-critical typos), covers all core steps without omissions, and enhances accessibility via annotated derivations. This automation reshapes telecommunication optimization education by lowering entry barriers for newcomers and streamlining research workflows by eliminating repetitive derivations, enabling researchers to focus on scenario modeling. While LLMs cannot replace manual verification for rigor, they democratize access to specialized optimization techniques. Conclusion: LLMs can serve as automated co-designers to facilitate LO design, reducing barriers to entry in this field and making it more accessible to non-expert users. Future work includes extending LLMs’ capabilities, exploring application scenarios, and developing hybrid co-design workflows.