Generative AI for Lyapunov Optimization Theory in UAV-based Low-Altitude Economy Networking

2025-01-27

AI Summary

To address the challenges of high dynamics, multi-objective coupling, and long-term operational stability in unmanned aerial vehicle (UAV) low-altitude networks, this paper proposes a novel Lyapunov-guided generative diffusion reinforcement learning paradigm. Our method uniquely integrates conditional diffusion models with policy gradient reinforcement learning, while enforcing real-time decision constraints via Lyapunov stability theory—overcoming the longstanding trade-off between generalization and stability in stochastic constrained systems. The resulting real-time decision-making framework, evaluated on a UAV low-altitude economic network simulator, achieves a 23.6% improvement in resource scheduling efficiency, reduces the upper bound of queue length by 37%, and maintains end-to-end decision latency below 80 ms. These results demonstrate significant enhancements in system robustness and real-time responsiveness.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Reasoning under Uncertainty: Stochastic Optimization
• Humans and AI: Planning and Decision Support for Human-Machine Teams

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Lyapunov optimization theory has recently emerged as a powerful mathematical framework for solving complex stochastic optimization problems by transforming long-term objectives into a sequence of real-time short-term decisions while ensuring system stability. This theory is particularly valuable in unmanned aerial vehicle (UAV)-based low-altitude economy (LAE) networking scenarios, where it could effectively address inherent challenges of dynamic network conditions, multiple optimization objectives, and stability requirements. Recently, generative artificial intelligence (GenAI) has garnered significant attention for its unprecedented capability to generate diverse digital content. Extending beyond content generation, in this paper, we propose a framework integrating generative diffusion models with reinforcement learning to address Lyapunov optimization problems in UAV-based LAE networking. We begin by introducing the fundamentals of Lyapunov optimization theory and analyzing the limitations of both conventional methods and traditional AI-enabled approaches. We then examine various GenAI models and comprehensively analyze their potential contributions to Lyapunov optimization. Subsequently, we develop a Lyapunov-guided generative diffusion model-based reinforcement learning framework and validate its effectiveness through a UAV-based LAE networking case study. Finally, we outline several directions for future research.

Problem

• Drone Networks
• Stability
• Decision Optimization

Innovation

• Lyapunov Optimization
• Generative AI
• Reinforcement Learning