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Metal alloy additive manufacturing (AM) has gained wide industrial interest in the past decade due to its capability to efficiently deliver complicated mechanical parts with high quality. However, due to a lack of understanding of the fundamental correlation between the operating conditions and build quality, the exploration of the optimal operating policy of the AM process is costly and difficult. In this work, a data-driven process optimization framework has been proposed for the additive manufacturing process, integrating machine learning, finite-element method (FEM) modeling, and cloud-edge data storage/transfer optimization. A three-level hierarchy of local machines, factory clouds, and a research center is introduced with each level responsible for its dedicated tasks. In addition, to ensure the efficiency of data transfer and storage, an edge-cloud data transfer scheme is constructed, which serves as a guideline for the data flow in the AM framework. Moreover, an overview of the connections between the proposed framework and the Industry 4.0 framework is presented.