Supplementary information for Efficient dynamic distributed resource slicing in 6G multi-access edge computing networks with online ADMM and message passing graph neural networks

<h2>Article abstract</h2><p dir="ltr">We consider the problem of resource slicing in the 6th generation multi-access edge computing (6G-MEC) network. The network includes many non-stationary space-air-ground-sea nodes with dynamic, unstable connections and resources, where any node can be in one of two hidden states: i) reliable - when the node generates/propagates no data errors; ii) unreliable - when the node can generate/propagate random errors. We show that solving this problem is challenging, since it represents a non-deterministic polynomial-time (NP) hard dynamic combinatorial optimization problem depending on the unknown distribution of hidden nodes' states and time-varying parameters (connections and resources of nodes) which can only be observed locally. To tackle these challenges, we develop a new deep learning (DL) model based on the message passing graph neural network (MPNN) to estimate hidden nodes' states in dynamic network environments. We then propose a novel algorithm based on the integration of MPNN-based DL and online alternating direction method of multipliers (ADMM) - extension of the well-known classical 'static' ADMM to dynamic settings, where the slicing problem is solved distributedly, in real time, based on local information. We prove that our algorithm converges to a global optimum of our problem with a superior performance even in the highly-dynamic, unreliable scenarios.</p><p dir="ltr">© 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.</p>