The improvements in the edge computing technology pave the road for diversified applications that demand real-time interaction. However, due to the mobility of the end-users and the dynamic edge environment, it becomes challenging to handle the task offloading with high performance. Considering the dynamics of the edge computing networks, the policy for task orchestration should be learned from the environment in order to make accurate decisions. Thus, we investigate the deep learning solutions including Deep Reinforcement Learning (DRL) and Federated Learning (FL) that are able to meet the dynamic needs of different application types under various loads in edge computing. This research is the main research subject for my PhD studies.