Inverse Reinforcement Learning With Graph Neural Networks for Full-Dimensional Task Offloading in Edge Computing

The ever-increasing number of ubiquitous Internet of Things (IoT) applications entails a high demand for scarce communication and network resources. To meet this stringent requirement, mobile edge computing (MEC) is envisioned as a transformative technique to significantly streamline the existing network operations. Recently, device-to-device (D2D) communication has been proposed as a promising technology in 5G and beyond networks with a significantly increased transmission efficiency, especially suitable for small-packet task exchanges. In this paper, we incorporate D2D communication into the multi-layer computing network and propose a full-dimensional task offloading scheme by jointly optimizing task offloading decisions and computation/communication resource allocation. We formulate it as mixed-integer nonlinear programming (MINLP) problem, where the optimal branch-and-bound (B$ \& amp; $B) algorithm with the full strong branching (FSB) variable selection policy features an extremely high complexity. To address this challenge, we propose inverse reinforcement learning with graph neural networks (GIRL) to generate a new variable selection policy that closely matches the FSB variable selection. Without sacrificing the global optimality, the GIRL can directly infer the variable selection with a much lower complexity, significantly accelerating the original B$ \& amp; $B algorithm. Simulation results show that the GIRL achieves a lower complexity without sacrificing the global optimality. Furthermore, our proposed full-dimensional task offloading scheme achieves better performance than the existing schemes in terms of average delay for all mobile devices (MDs).