Scalable Resource Management for Dynamic MEC: An Unsupervised
  Link-Output Graph Neural Network Approach
Deep learning has been successfully adopted in mobile edge computing (MEC) to
optimize task offloading and resource allocation. However, the dynamics of edge
networks raise two challenges in neural network (NN)-based optimization
methods: low scalability and high training costs. Although conventional
node-output graph neural networks (GNN) can extract features of edge nodes when
the network scales, they fail to handle a new scalability issue whereas the
dimension of the decision space may change as the network scales. To address
the issue, in this paper, a novel link-output GNN (LOGNN)-based resource
management approach is proposed to flexibly optimize the resource allocation in
MEC for an arbitrary number of edge nodes with extremely low algorithm
inference delay. Moreover, a label-free unsupervised method is applied to train
the LOGNN efficiently, where the gradient of edge tasks processing delay with
respect to the LOGNN parameters is derived explicitly. In addition, a
theoretical analysis of the scalability of the node-output GNN and link-output
GNN is performed. Simulation results show that the proposed LOGNN can
efficiently optimize the MEC resource allocation problem in a scalable way,
with an arbitrary number of servers and users. In addition, the proposed
unsupervised training method has better convergence performance and speed than
supervised learning and reinforcement learning-based training methods. The code
is available at \url{https://github.com/UNIC-Lab/LOGNN}.
Xiucheng Wang, Nan Cheng, Lianhao Fu, Wei Quan, Ruijin Sun, Yilong Hui, Tom Luan, Xuemin Shen
Scalable Resource Management for Dynamic MEC: An Unsupervised Link-Output Graph Neural Network Approach

###### Abstract

Deep learning has been successfully adopted in mobile edge computing (MEC) to optimize task offloading and resource allocation. However, the dynamics of edge networks raise two challenges in neural network (NN)-based optimization methods: low scalability and high training costs. Although conventional node-output graph neural networks (GNN) can extract features of edge nodes when the network scales, they fail to handle a new scalability issue whereas the dimension of the decision space may change as the network scales. To address the issue, in this paper, a novel link-output GNN (LOGNN)-based resource management approach is proposed to flexibly optimize the resource allocation in MEC for an arbitrary number of edge nodes with extremely low algorithm inference delay. Moreover, a label-free unsupervised method is applied to train the LOGNN efficiently, where the gradient of edge tasks processing delay with respect to the LOGNN parameters is derived explicitly. In addition, a theoretical analysis of the scalability of the node-output GNN and link-output GNN is performed. Simulation results show that the proposed LOGNN can efficiently optimize the MEC resource allocation problem in a scalable way, with an arbitrary number of servers and users. In addition, the proposed unsupervised training method has better convergence performance and speed than supervised learning and reinforcement learning-based training methods. The code is available at [https://github.com/UNIC-Lab/LOGNN](https://github.com/UNIC-Lab/LOGNN).

 edge computing, link-output graph neural network, scalability, unsupervised learning

## I Introduction

In recent years, mobile edge computing (MEC) has garnered widespread attention for its ability to reduce task processing latency by providing edge computing resources to users with limited computing capabilities [1]. The conventional approach involves transmitting user tasks to the server via a wireless network, with several variables optimized to minimize task computing delays, such as offloading proportion, user transmission power, and server computing resource allocation, among others. Given the critical role of MEC in enhancing user experience, numerous researchers have focused their efforts on designing resource management methods that can further optimize MEC performance [2, 3]. Drawing inspiration from the remarkable achievements of deep learning, several studies have employed neural networks (NN) to address the optimization problem in MEC, outperforming traditional optimization methods both in terms of performance and algorithm execution time [4, 5].

The dynamics of MEC systems, which are changes in numbers and locations of the edge servers (e.g., flying drones as MEC servers) and users (e.g., vehicular users), raise two challenges in NN-based methods: low scalability and high training costs [6]. Scalability plays a crucial role in determining whether a new NN architecture needs to be manually designed and retrained when the number of edge servers and users undergoes changes. Additionally, training costs are a key factor in determining the ability of an NN-based method to be rapidly deployed in the edge network. Some recent works explore using graph neural network (GNN) to deal with the scalability issue in input space, which includes usually the features of network nodes. This is because the inference of GNN relies on the message passing method which is an input dimension-independent method [7, 8]. However, in MEC, the dimension of offloading and resource allocation decisions can also change as the network scales. For instance, a task can be offloaded to a varying number of servers, thereby leading to a unique scalability issue, i.e., scalability in the decision space. Unfortunately, the conventional node-output GNN, which allocates resources from an edge node to others through the dimension-fixed node features vector, fails to address the dimension change of the decision space caused by the changing size of the edge network. Thus, the development of a novel approach that can efficiently tackle the scalability issues in both input and decision space remains a crucial area of research in optimizing MEC.

This paper presents a novel resource management scheme for dynamic MEC that leverages the capabilities of a link-output Graph Neural Network (LOGNN). Despite the fixed dimension of output link features, the number of graph links increases as the number of edge servers and users increases.