Bridging Control Theory and Machine Learning

The design of modern intelligent systems relies heavily on techniques developed in the control and machine learning communities. On one hand, control techniques are crucial for safety-critical systems; the robustness to uncertainty and disturbance is typically introduced by a model-based design equipped with sensing, actuation, and feedback. On the other hand, learning techniques have achieved the state-of-the-art performance for a variety of artificial intelligence tasks (computer vision, natural language processing, and Go). The developments of next-generation intelligent systems such as self-driving cars, advanced robotics, and smart buildings require leveraging these control and learning techniques in an efficient and safe manner.

This talk will focus on fundamental connections between robust control and machine learning. Specifically, we will present a control perspective on the empirical risk minimization (ERM) problem in machine learning. ERM is a central topic in machine learning research, and is typically solved using first-order optimization methods which are developed in a case-by-case manner. First, we will discuss how to adapt robust control theory to automate the analysis of such optimization methods including the gradient descent method, Nesterov's accelerated method, stochastic gradient descent (SGD), stochastic average gradient (SAG), SAGA, Finito, stochastic dual coordinate ascent (SDCA), stochastic variance reduction gradient (SVRG), and Katyusha momentum. Next, we will show how to apply classical control design tools (Nyquist plots and multiplier theory) to develop new robust accelerated methods for ERM problems. Finally, we will conclude with some long-term research vision on the general connections between our proposed control-oriented tools and reinforcement learning methods.