GDSG: Graph Diffusion-based Solution Generator for Optimization Problems in MEC Networks

TL;DR

This work targets NP-hard optimization in MEC networks where optimal solutions are scarce. It introduces Graph Diffusion-based Solution Generator (GDSG), which learns a distribution over feasible solutions from suboptimal data via a graph-diffusion framework, enabling parallel sampling toward near-optimality. GDSG employs a GNN backbone with a padding-edge gating mechanism and a multi-task diffusion setup that jointly handles discrete offloading decisions and continuous resource allocations, achieving strong orthogonality between tasks and fast inference via DDIM. Theoretical analysis connects suboptimal data quality to convergence toward the optimum, and experiments show GDSG often surpasses discriminative baselines and reduces total cost by substantial margins on large-scale MSCO instances. The approach provides a practical, data-efficient path to robust network optimization, supported by open-source MSCO datasets and code.

Abstract

Optimization is crucial for MEC networks to function efficiently and reliably, most of which are NP-hard and lack efficient approximation algorithms. This leads to a paucity of optimal solution, constraining the effectiveness of conventional deep learning approaches. Most existing learning-based methods necessitate extensive optimal data and fail to exploit the potential benefits of suboptimal data that can be obtained with greater efficiency and effectiveness. Taking the multi-server multi-user computation offloading (MSCO) problem, which is widely observed in systems like Internet-of-Vehicles (IoV) and Unmanned Aerial Vehicle (UAV) networks, as a concrete scenario, we present a Graph Diffusion-based Solution Generation (GDSG) method. This approach is designed to work with suboptimal datasets while converging to the optimal solution large probably. We transform the optimization issue into distribution-learning and offer a clear explanation of learning from suboptimal training datasets. We build GDSG as a multi-task diffusion model utilizing a Graph Neural Network (GNN) to acquire the distribution of high-quality solutions. We use a simple and efficient heuristic approach to obtain a sufficient amount of training data composed entirely of suboptimal solutions. In our implementation, we enhance the backbone GNN and achieve improved generalization. GDSG also reaches nearly 100\% task orthogonality, ensuring no interference between the discrete and continuous generation tasks. We further reveal that this orthogonality arises from the diffusion-related training loss, rather than the neural network architecture itself. The experiments demonstrate that GDSG surpasses other benchmark methods on both the optimal and suboptimal training datasets. The MSCO datasets has open-sourced at this http URL, as well as the GDSG algorithm codes at https://github.com/qiyu3816/GDSG.

Figures (8)

• Figure 1: System model of multi-server and multi-user computation offloading.
• Figure 2: Framework for training the diffusion generative model with suboptimal dataset to achieve the optimal solution generation.
• Figure 3: The expectation of hitting $\mathbf{y}^*$ for different number of samples $n$ and variable dimension $N$. The dotted lines represent the lower bounds on $n$, where the red and black dotted lines coincide.
• Figure 4: Left: The cosine value of the overall average of all relevant parameters (The closer to 1, the better the orthogonality). Right: The proportion of the orthogonal vector for a given range in a training step (The closer to 100%, the better the orthogonality).
• Figure 5: The performance Exceed_ratio of GDSG (GNN padding edge not handled).