Distributed machine learning (ML) systems can enable a variety of new applications in health-care, autonomous vehicles, smart cities, robotics, etc. However, distributed ML faces several systems and algorithmic challenges including communication bandwidth, systems heterogeneity, data heterogeneity, adversarial perturbations, and scalability. Our research leverages tools from optimization theory and information theory to tackle these challenges, and develop provably efficient algorithms with strong statistical performance guarantees for the machine learning model. In particular, we aim at developing fast, robust, and private federated learning and collaborative learning algorithms that achieve optimal performance in terms of convergence rate for both convex and non-convex settings. In another project, we focus on human-cyber-physical-systems (h-CPS) such as next-generation transportation systems that involve both human and robot agents. Our research leverages tools from reinforcement and game theory for data-driven efficient control and management of h-CPS.