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.

Generative AI (GenAI) has emerged as a transformative technology, enabling customized and personalized AI-generated content (AIGC) services. In this paper, we address challenges of edge-enabled AIGC service provisioning, which remain underexplored in the literature. These services require executing GenAI models with billions of parameters, posing significant obstacles to resource-limited wireless edge. We subsequently introduce the formulation of joint model caching and resource allocation for AIGC services to balance a trade-off between AIGC quality and latency metrics. We obtain mathematical relationships of these metrics with the computational resources required by GenAI models via experimentation. Afterward, we decompose the formulation into a model caching subproblem on a long-timescale and a resource allocation subproblem on a short-timescale. Since the variables to be solved are discrete and continuous, respectively, we leverage a double deep Q-network (DDQN) algorithm to solve the former subproblem and propose a diffusion-based deep deterministic policy gradient (D3PG) algorithm to solve the latter. The proposed D3PG algorithm makes an innovative use of diffusion models as the actor network to determine optimal resource allocation decisions. Consequently, we integrate these two learning methods within the overarching two-timescale deep reinforcement learning (T2DRL) algorithm, the performance of which is studied through comparative numerical simulations.

The rapid advancement of Artificial Intelligence (AI) has introduced Deep Neural Network (DNN)-based tasks to the ecosystem of vehicular networks. These tasks are often computation-intensive, requiring substantial computation resources, which are beyond the capability of a single vehicle. To address this challenge, Vehicular Edge Computing (VEC) has emerged as a solution, offering computing services for DNN-based tasks through resource pooling via Vehicle-to-Vehicle/Infrastructure (V2V/V2I) communications. In this paper, we formulate the problem of joint DNN partitioning, task offloading, and resource allocation in VEC as a dynamic long-term optimization. Our objective is to minimize the DNN-based task completion time while guaranteeing the system stability over time. To this end, we first leverage a Lyapunov optimization technique to decouple the original long-term optimization with stability constraints into a per-slot deterministic problem. Afterwards, we propose a Multi-Agent Diffusion-based Deep Reinforcement Learning (MAD2RL) algorithm, incorporating the innovative use of diffusion models to determine the optimal DNN partitioning and task offloading decisions. Furthermore, we integrate convex optimization techniques into MAD2RL as a subroutine to allocate computation resources, enhancing the learning efficiency. Through simulations under real-world movement traces of vehicles, we demonstrate the superior performance of our proposed algorithm compared to existing benchmark solutions.

Vehicular clouds (VCs) are modern platforms for processing of computation-intensive tasks over vehicles. Such tasks are often represented as directed acyclic graphs (DAGs) consisting of interdependent vertices/subtasks and directed edges. In this paper, we propose a graph neural network-augmented deep reinforcement learning scheme (GA-DRL) for scheduling DAG tasks over dynamic VCs. In doing so, we first model the VC-assisted DAG task scheduling as a Markov decision process. We then adopt a multi-head graph attention network (GAT) to extract the features of DAG subtasks. Our developed GAT enables a two-way aggregation of the topological information in a DAG task by simultaneously considering predecessors and successors of each subtask. We further introduce non-uniform DAG neighborhood sampling through codifying the scheduling priority of different subtasks, which makes our developed GAT generalizable to completely unseen DAG task topologies. Finally, we augment GAT into a double deep Q-network learning module to conduct subtask-to-vehicle assignment according to the extracted features of subtasks, while considering the dynamics and heterogeneity of the vehicles in VCs. Through simulating various DAG tasks under real-world movement traces of vehicles, we demonstrate that GA-DRL outperforms existing benchmarks in terms of DAG task completion time.