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This thesis develops data-driven machine learning algorithms to managing and optimizing the next-generation highly complex cyberphysical systems, which desperately need ground-breaking control, monitoring, and decision making schemes that can guarantee robustness, scalability, and situational awareness. The present thesis first develops principled methods to make generic machine learning models robust against distributional uncertainties and adversarial data. Particular focus will be on parametric models where some training data are being used to learn a parametric model. The developed framework is of high interest especially when training and testing data are drawn from "slightly" different distribution. We then introduce distributionally robust learning frameworks to minimize the worst-case expected loss over a prescribed ambiguity set of training distributions quantified via Wasserstein distance. Later, we build on this robust framework to design robust semi-supervised learning over graph methods. The second part of this thesis aspires to fully unleash the potential of next-generation wired and wireless networks, where we design "smart" network entities using (deep) reinforcement learning approaches. Finally, this thesis enhances the power system operation and control. Our contribution is on sustainable distribution grids with high penetration of renewable sources and demand response programs. To account for unanticipated and rapidly changing renewable generation and load consumption scenarios, we specifically delegate reactive power compensation to both utility-owned control devices (e.g., capacitor banks), as well as smart inverters of distributed generation units with cyber-capabilities.