This paper studies mobile edge computing (MEC) networks where multiple wireless devices (WDs) offload their computation tasks to multiple edge servers and one cloud server. Considering different real-time computation tasks at different WDs, every task is decided to be processed locally at its WD or to be offloaded to and processed at one of the edge servers or the cloud server. In this paper, we investigate low-complexity computation offloading policies to guarantee quality of service of the MEC network and to minimize WDs’ energy consumption. Specifically, both a linear programing relaxation-based (LR-based) algorithm and a distributed deep learning-based offloading (DDLO) algorithm are independently studied for MEC networks. We further propose a heterogeneous DDLO to achieve better convergence performance than DDLO. Extensive numerical results show that the DDLO algorithms guarantee better performance than the LR-based algorithm. Furthermore, the DDLO algorithm generates an offloading decision in less than 1 millisecond, which is several orders faster than the LR-based algorithm.