A Lyapunov-Guided Diffusion-Based Reinforcement Learning Approach for UAV-Assisted Vehicular Networks with Delayed CSI Feedback

Zhang Liu, Lianfen Huang, Zhibin Gao, Xianbin Wang, Dusit Niyato, Xuemin ShenarXiv 2025 · DOI · OpenReview

TL;DR

This paper introduces a novel approach, D3PG, for optimizing UAV-assisted vehicular networks. By combining Lyapunov optimization with a diffusion-based reinforcement learning agent, it effectively manages network resources and UAV trajectories to maximize communication rates while ensuring the UAV's long-term energy efficiency, even with delayed channel information.

What Problem Does This Paper Address?

The integration of Unmanned Aerial Vehicles (UAVs) into intelligent transportation systems promises to enhance connectivity and unlock the "low-altitude economy." However, several challenges hinder this vision. Firstly, optimizing network resources (like channel allocation and power control) and UAV flight paths in real-time for highly dynamic vehicular environments is complex. Secondly, UAVs have limited battery life, necessitating a balance between maximizing communication performance and conserving energy over extended periods. Thirdly, obtaining accurate Channel State Information (CSI) is difficult due to factors like Doppler effects and feedback delays, which can significantly degrade performance if not properly handled. Existing methods struggle to address these interconnected challenges simultaneously, especially in dynamic, real-world scenarios.

Methods

The paper proposes a two-pronged approach:

  1. Lyapunov Optimization: To tackle the long-term energy constraint and the interdependence of decisions across time, the authors employ Lyapunov optimization. This technique decomposes the complex, long-term optimization problem into a series of simpler, per-slot deterministic subproblems. It introduces a "virtual queue" to track the UAV's accumulated energy cost, ensuring it stays within a threshold.
  2. Diffusion-Based Deep Deterministic Policy Gradient (D3PG): For the per-slot optimization, a novel DRL algorithm called D3PG is introduced.
  3. Diffusion Models for Action Generation: Instead of traditional Multi-Layer Perceptrons (MLPs) in the actor network, D3PG utilizes diffusion models. These models, typically used for image generation, are adapted here to "generate" optimal decisions for channel allocation, power control, and UAV altitude adjustment. The diffusion process allows for a more robust exploration-exploitation trade-off and better adaptation to dynamic environments with delayed CSI.
  4. Deep Deterministic Policy Gradient (DDPG) Foundation: D3PG builds upon the DDPG framework, which uses separate actor and critic networks. The actor proposes actions (decisions), and the critic evaluates them. D3PG enhances the actor network with the diffusion model.
  5. Action Amender: A post-processing step ensures that the generated actions adhere to all defined constraints (e.g., channel assignment rules, power limits, altitude ranges).

Datasets

The paper uses simulated data generated from a realistic network environment.

  • Network Layout: A 2 km, one-way highway segment in Xiamen, China, sourced from OpenStreetMap.
  • Vehicle Mobility: Simulated using the SUMO (Simulation of Urban Mobility) simulator, incorporating real-world vehicle traces.
  • UAV Behavior: A single UAV acts as an aerial base station, moving at a constant speed of 50 km/h to follow ground vehicles.

No specific pre-existing datasets for training were mentioned; the evaluation is based on simulations.

Key Insights and Ideas

  • Diffusion Models as Policy Generators: The core innovation is using diffusion models not just for generating data but for generating optimal control policies in a DRL context. This allows for a more nuanced and robust decision-making process compared to traditional MLPs.
  • Handling CSI Delay with Diffusion: The diffusion model's ability to be conditioned on the current state (including delayed CSI) allows it to adapt and generate more accurate actions, mitigating the performance degradation typically associated with CSI inaccuracies.
  • Lyapunov Optimization for Long-Term Constraints: Decomposing the problem using Lyapunov optimization is crucial for managing the UAV's finite energy budget over extended operation periods, a critical factor for practical deployment.
  • Balancing V2U Rate and UAV Energy: The Lyapunov weight parameter (V) effectively controls the trade-off between maximizing V2U communication rates and minimizing UAV energy consumption, allowing for flexible system tuning.

Key Results

  • Superior Performance: The proposed D3PG algorithm consistently outperformed benchmark solutions (DDPG, D3PG-WCSI, H-DDQN) in terms of V2U communication sum rate. For instance, with 10 V2V links, D3PG achieved improvements of 6.39% over D3PG-WCSI, 12.55% over DDPG, and 23.25% over H-DDQN.
  • Robustness to CSI Delay: D3PG showed significantly better performance than D3PG-WCSI (which ignores CSI delay) as CSI feedback delay increased, demonstrating the effectiveness of its approach to handle outdated information.
  • Energy Efficiency: The UAV's long-term energy consumption remained below the predefined threshold for all methods, but D3PG achieved this with a lower average energy consumption (e.g., 2.15% lower than D3PG-WCSI).
  • Impact of V2V Links: Increasing the number of V2V links (and thus spectrum reuse) negatively impacted the V2U sum rate due to increased interference, a challenge D3PG managed more effectively.
  • Denoising Step Impact: The number of denoising steps in the diffusion model was found to be critical for performance, with an optimal range identified (I=4 in their experiments).

Limitations and Future Work

  • Computational Complexity: While D3PG offers superior performance, its computational complexity is higher than simpler DRL methods due to the iterative nature of the diffusion model's reverse process. The paper notes this is manageable as training can occur in cloud data centers.
  • Single UAV Assumption: The current framework assumes a single UAV.
  • Future Work: The authors suggest extending the framework to multi-UAV scenarios, which introduces additional complexities related to inter-UAV coordination and distributed energy management.
BibTeX
@misc{liu2025lyapunov,
  author = {Zhang Liu and Lianfen Huang and Zhibin Gao and Xianbin Wang and Dusit Niyato and Xuemin Shen},
  title = {{A Lyapunov-Guided Diffusion-Based Reinforcement Learning Approach for UAV-Assisted Vehicular Networks with Delayed CSI Feedback}},
  year = {2025},
  eprint = {2507.20524},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2507.20524},
}