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

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.