As a promising computing paradigm, mobile edge computing can sink the computing resources from the cloud center into the edge of the network, consequently enhancing the ability of data processing. To meet the real-time requirements of some computation-intensive tasks in the end devices, e.g., face recognition, video analysis, etc., the resource-constrained end devices require to offload the tasks to the edge nodes with more computing resources. In order to optimize the offloading decisions, the status information defined as status of the available computation capacity held by the end devices becomes critical. If the status held by the end devices is stale, i.e., the Age-of-Information (AoI) is high, it is impossible to make effective offloading decisions. In this paper, we formulate a problem of maximizing the average computation rate of the edge system. It is decomposed into several sub-problems, including detection action optimization and offloading action optimization. A node sorting algorithm based on status and AoI is proposed to optimize the detection sequence. Then, a threshold-based nodes' status detection algorithm is devised. In addition, we propose an AoI-aware detected proximal policy optimization framework (ADPPO) to optimize the offloading decisions based on status information and AoI. The numerical results show that the proposed framework outperforms other offloading algorithms in terms of the average computation rate.