In this article, a deep reinforcement learning (DRL) control scheme is proposed to satisfy the strict Quality-of-Service (QoS) requirements of ultrareliability low-latency communication (URLLC) and enhanced mobile broadband (eMBB) using 5G multiple radio access technology (RAT)-based partial offloading and multiaccess edge-computing (MEC) resource allocation. In the proposed scheme, the user equipment (UE) makes optimal offloading decisions while the MEC server dynamically adjusts the server resources based on offloading requests from multiple UEs using DRL technology. The aim of the proposed scheme is to minimize the energy consumption of the UEs while maximizing the system utility (SU) performance, which is composed of the spectral efficiency (SE) and offloading success rate (OSR) of the MEC server. In addition, multiagent distributed learning technology and best experience push (BEP) techniques are used to enhance the learning efficiency of the DRL framework. The simulation result shows that the proposed scheme provides an improved SU and energy consumption performance compared to the benchmark offloading schemes.