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As an emerging technique, mobile edge computing (MEC) introduces a new processing scheme for various distributed communication-computing systems such as industrial Internet of Things (IoT), vehicular communication, smart city, etc. In this work, we mainly focus on the timeliness of the MEC systems where the freshness of the data and computation tasks is significant. Firstly, we formulate a kind of age-sensitive MEC models and define the average age of information (AoI) minimization problems of interests. Then, a novel policy based multi-agent deep reinforcement learning (RL) framework, called heterogeneous multi-agent actor critic (H-MAAC), is proposed as a paradigm for joint collaboration in the investigated MEC systems, where edge devices and center controller learn the interactive strategies through their own observations. To improves the system performance, we develop the corresponding online algorithm by introducing an edge federated learning mode into the multi-agent cooperation whose advantages on learning convergence can be guaranteed theoretically. To the best of our knowledge, it's the first joint MEC collaboration algorithm that combines the edge federated mode with the multi-agent actor-critic reinforcement learning. Furthermore, we evaluate the proposed approach and compare it with classical RL based methods. As a result, the proposed framework not only outperforms the baseline on average system age, but also promotes the stability of training process. Besides, the simulation results provide some innovative perspectives for the system design under the edge federated collaboration.