Harnessing the power of data collected from a vast amount of geographically distributed and heterogeneous devices, in a manner without moving data around and violating privacy, has great potential in advancing science and technology and improving quality of life. Federated optimization lies at the heart of the practice realizing this vision, encompassing problems such as training large-scale machine learning or artificial intelligence models, delivering insightful data analytics, as well as facilitating decision making under uncertainty, all in distributed manners. There is a significant gap in the algorithmic foundation of federated optimization when interfacing with bandwidth-limited heterogeneous networks, such as internet-of-things, smart healthcare, and edge computing, to meet the unique challenges of taming heterogeneity, privacy, and uncertainty without sacrificing efficiency. This research project will also be tightly integrated with education and workforce developments, through offering new courses, mentoring students at all levels in research projects, and disseminating the research outcomes at suitable conferences and workshops. The goal of the research program is to develop a federated optimization framework to learning and decision making by designing communication-efficient, computation-scalable, and privacy-preserving algorithms that converge provably over highly heterogeneous data and computing environments. Leveraging insights from machine learning, optim