CAREER: Interplay between Control Theory and Machine Learning

控制和机器学习是两个影响很大的研究领域。两者对于管理复杂系统（如自动驾驶汽车、人形机器人、智能建筑和自动化医疗保健）都很重要。这个CAREER提案旨在建立控制理论和机器学习之间的基本联系。一方面，控制理论为解决现代安全关键系统（如商用飞机和核电站）的鲁棒性要求提供了数学上严格的工具。另一方面，机器学习技术已被用于在计算机视觉、自然语言处理和围棋等许多人工智能任务中实现最先进的性能。控制理论和机器学习的结合将极大地拓宽可有效解决的工程问题类别。本提案旨在通过一种全面的跨学科方法来协调这两个领域，该方法跨越并连接鲁棒控制理论、非线性系统理论、跳跃系统理论、监督学习、强化学习、模仿学习、半确定规划和非凸优化的前沿。提出的研究将为现代安全关键智能系统中控制和机器学习的可靠集成奠定理论基础。研究进展将促进多学科合作，并使研究人员从学习，控制，优化，人工智能，自主和机器人技术中受益。此外，研究将与教育发展紧密结合，促进不同院系的学生培养扎实的多学科能力。新教材的研究将提供新的概念和想法，以激励下一代的学术和工业领袖。本提案从跨学科的角度研究机器学习和控制。拟议的研究主要围绕两个重点。第一个重点是裁剪控制理论，以统一、简化和自动化机器学习算法的分析和设计。具体来说，监督/强化/无监督学习中的算法将被建模为控制文献中广泛研究的马尔可夫跳跃系统和非线性系统。将这一思想与现代控制理论工具（如随机耗散不等式）相结合，将为机器学习中高性能算法管道设计的统一原则方法铺平道路。第二个重点是借鉴非凸学习的最新成果，推动控制理论超越凸优化机制。本文将利用近年来发展起来的非凸学习理论，为控制中的非凸优化问题提供各种理论保证。所提出的研究有望推动大规模控制中最先进的算法，并扩大可以用保证解决的非线性/鲁棒控制问题的类别。拟议的研究涵盖了“为学习而控制”和“为控制而学习”，通过展示双方使用的技术可以被探索以影响另一方，加深了控制和学习的联系。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.