Network Function Virtualization (NFV) and Multi-access Edge Computing (MEC) are two technologies expected to play a vital role in 5G and beyond networks. However, adequate mechanisms are required to meet the dynamically changing network service demands to utilize the network resources optimally and also to satisfy the demanding QoS requirements. Particularly in multi-domain scenarios, the additional challenge of isolation and data privacy among domains needs to be tackled. To this end, centralized and distributed Artificial Intelligence (AI)-driven resource orchestration techniques (e.g., virtual network function (VNF) autoscaling) are foreseen as the main enabler. In this work, we propose deep learning models, both centralized and federated approaches, that can perform horizontal and vertical autoscaling in multi-domain networks. The problem of autoscaling is modelled as a time series forecasting problem that predicts the future number of VNF instances based on the expected traffic demand. We evaluate the performance of various deep learning models trained over a commercial network operator dataset and investigate the pros and cons of federated learning over centralized learning approaches. Furthermore, we introduce the AI-driven Kubernetes orchestration prototype that we implemented by leveraging our MEC platform and assess the performance of the proposed deep learning models in a practical setup.