Mobile edge computing (MEC) provides an effective solution to help the Internet of Things (IoT) devices with delay-sensitive and computation-intensive tasks by offering computing capabilities in the proximity of mobile device users. Most of the existing studies ignore context information of the application, requests, sensors, resources, and network. However, in practice, context information has a significant impact on offloading decisions. In this paper, we consider context-aware offloading in MEC with multi-user. The contexts are collected using autonomous management as the MAPE loop in all offloading processes. Also, federated learning (FL)-based offloading is presented. Our learning method in mobile devices (MDs) is deep reinforcement learning (DRL). FL helps us to use distributed capabilities of MEC with updated weights between MDs and edge devices (Eds). The simulation results indicate our method is superior to local computing, offload, and FL without considering context-aware algorithms in terms of energy consumption, execution cost, network usage, delay, and fairness. © 2021, The Author(s), under exclusive licence to Springer Nature B.V.