<p>With the large-scale occurrence of emerging new applications and computationally-intensive applications, the mobile edge cloud computing mode assisted by cloud data centers is further prevalent. From the user’s view, how to prolong battery lifespan and reduce system delay is an urgent problem. From the service provider’s view, the long-term cost and makespan are the focus points of offloading in such an edge cloud computing environment. The mobile edge cloud computing paradigm is suffering from the problem that the offloading needs are so diverse that it cannot take into account the high-dimensional optimization objectives. Edge offloading faces the challenge of objective diversification and high dimension. The first-phase offloading is purposed to judge which tasks should be executed locally according to the energy consumption and system delay tradeoff; the second-phase offloading is purposed to offload excessive tasks to the edge or central cloud according to the cost and makespan tradeoff. In this study, we introduce DARQN (deep attention recurrent Q-Network) for less training time, and put more attentions on the relevant one in high-dimensional state inputs. The attention mechanism is introduced to focus on the information that is more critical to the current task among the numerous input information, reduce attention to other information, and even filter out irrelevant information. We introduce an attention mechanism in deep recurrent Q-network to learn offloading policy via selective attention to the higher-dimensional input state. Abundant contrast experiments and parameter calibration experiments demonstrate the effectiveness and efficiency of the proposed algorithm.</p>