The paradigm of the Internet of Things (IoT) and cloud-edge computing plays a significant role in future smart grids. The data-driven solution integrating the artificial intelligence functionalities brings novel methods to address the nontrivial task of economic dispatch in microgrids in the presence of uncertainties of renewable generations and loads. This article proposes a learning-based decision-making framework for the economic energy dispatch of an islanding microgrid based on the cloud-edge computing architecture. Cloud resources are utilized to solve the optimal dispatch decision sequences over historical operating patterns. It can be considered as a sample labeling process for the supervised training that can implement the complex mapping of input-output space through an advanced machine learning model. Then, the well-trained model can be adopted locally at edge computing devices keeping the long-term parameters unchanged for implement the real-time microgrid energy dispatch. The key benefit of the proposed solution is that it effectively avoids the prediction of multiple stochastic variables and the design of sophisticated regulation strategies or reward policy functions for real-time dispatch. The solution is extensively assessed through simulation experiments by the use of real data measurements for a set of operational scenarios and the numerical results validate the effectiveness and benefit of the proposed algorithmic solution.