The explosive growth of machine learning and data-driven methodologies have revolutionized numerous fields. Yet, the translation of these successes to the domain of dynamical physical systems remains a significant challenge. Closing the loop from data to actions in these systems faces many difficulties, stemming from the need for sample efficiency and computational feasibility, along with many other requirement such as verifiability, robustness, and safety. In this talk, we bridge this gap by introducing innovative representations to develop nonlinear stochastic control and reinforcement learning methods. Key in the representation is to represent the stochastic, nonlinear dynamics linearly onto a nonlinear feature space. We present a comprehensive framework to develop control and learning strategies which achieve efficiency, safety, robustness, and scalability with provable performance. We also show how the representation could be used to close the sim-to-real gap. Lastly, we will briefly present some concrete real-world applications, discussing how domain knowledge is applied in practice to further close the loop from data to actions.
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