Scalability, flexibility, and maintaining Service Level Agreements (SLA) are primary goals in service management. Multi-access Edge Computing (MEC) in beyond-5G and 6G networks presents challenges in meeting these needs due to the increasing and variable demands generated by dynamic use cases. To tackle these issues, our objective is to design approaches to manage dynamicity regarding change in service demands and changing infrastructures in distributed MEC systems. We envision two methods: Distributed Deep Reinforcement Learning (DDRL) and Meta Reinforcement Learning (MRL), due to their ability to perform well in handling changing scenarios.