CAREER: Interplay between Control Theory and Machine Learning

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Control and machine learning are two high-impact research areas. Both are important for managing complex systems such as self-driving vehicles, humanoid robotics, smart buildings, and automated healthcare. This CAREER proposal aims at building fundamental connections between control theory and machine learning. On one hand, control theory provides mathematically rigorous tools for addressing the robustness requirement of modern safety-critical systems such as commercial aircraft and nuclear plants. On the other hand, machine learning techniques have been used to achieve the state-of-the-art performance for many artificial intelligence tasks in computer vision, natural language processing, and Go. A rapprochement of control theory and machine learning will significantly broaden the class of engineering problems that can be solved efficiently. This proposal aims at reconciling these two areas with a comprehensive interdisciplinary approach that spans and connects the forefronts of robust control theory, nonlinear system theory, jump system theory, supervised learning, reinforcement learning, imitation learning, semidefinite programming, and non-convex optimization. The proposed research will lay the theoretical foundation for reliable integration of control and machine learning in modern safety-critical intelligent systems. The research progress will promote multidisciplinary collaborations and benefit the researchers from learning, control, optimization, artificial intelligence, autonomy, and robotics. In addition, the research will be strongly coupled with educational developments which will promote students from different departments to develop solid multidisciplinary proficiency. New course materials resulting from the research will provide new concepts and ideas to inspire the next generation of academic and industrial leaders.This proposal takes an interdisciplinary perspective on machine learning and control. The proposed research is centered around two thrusts. The first thrust focuses on tailoring control theory to unify, streamline, and automate the analysis and design of machine learning algorithms. Specifically, algorithms in supervised/reinforcement/unsupervised learning will be modeled as Markovian jump systems and nonlinear systems which have been extensively studied in controls literature. The combination of this idea with modern control-theoretical tools such as stochastic dissipation inequalities will pave the way for a unified principled approach to the design of high-performance algorithmic pipelines in machine learning. The second thrust focuses on borrowing recent results in non-convex learning to push control theory beyond the convex optimization regime. The recently developed non-convex learning theory will be leveraged to derive various theoretical guarantees for non-convex optimization problems in control. The proposed research is expected to advance the state-of-the-art algorithms in large-scale control and broaden the class of nonlinear/robust control problems that can be solved with guarantees. The proposed research covers both “control for learning” and “learning for control,” deepening the connections of control and learning by showing that the techniques used by each side can be explored to impact the other side.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.