<p>With the explosion of diverse mobile applications, there are many critical issues to be solved in achieving the Quality of Experience (QoE) oriented and resource-efficient task offloading in container based Mobile Edge Computing (MEC) environments. In modern computing, users are all too frequently left behind the curve by incomplete computing techniques. As such, the aim of this study is to present a new framework that can overcome the limitations with current systems. Thus, this work, proposes a model-based machine teaching approach in the context of Federated Deep Reinforcement Learning (FDRL) to facilitate intelligent, adaptive and secure task offloading for heterogeneous edge nodes. With this design, an extensive optimization approach is embedded in containerized MEC systems to strike a balance between latency, energy and service disruption. This lightweight model enables Knowledge Distillation (KD) and efficient offloading of a task to devices with limited resources, without the need for full retraining. Because this is federated and using KD the framework provides a more advanced model to perform offloading in intricate and dynamic settings. Furthermore, the paper shows that this approach to offloading allows secure federated updates, making them efficient in both communication terms and in terms of bandwidth usage. In this way the time for convergence is greatly reduced. There is evidence to show that the framework incorporating FDRL with KD as presented in the paper can be found to be 20 percent higher in QoE, has an average task completion delay of 42 percent less, and 43 percent reduction for energy consumption per task compared with traditional methods. These are the results the paper found and thus underscore framework's correctness for high-performance, next-generation edge intelligence in mobile computing systems.</p>