Research Interests

Interests

I am interested in the general areas of control, machine learning and robotics. Below are several research topics we are currently looking into.

• Deep Learning and Statistical Physics: From a statistical point of view, over-parametrization of deep neural networks (DNN's) is at odds with their effectiveness in practice. One possible way to understand this is through the lens of statistical physics. The interplay between microscopic and macroscopic behavior may explain emergence of structure, and explain the apparent effectiveness of DNN’s.

• Theoretical Foundation of Reinforcement Learning: Reinforcement learning (RL) has demonstrated its magic power during the last decade, however, our understanding of RL has fallen behind. Compared to supervise learning, the theory for RL is scarce. Many challenges remain until RL can be used in safety-critical domains.

• General Purpose Robots: The goal is to develop theoretical foundations and algorithms for robots so that they are able to accomplish complex tasks autonomously and reliably. I plan to utilize tools from both control and machine learning to approach this goal.

• Uncertainty Synthesis: Uncertainty is ubiquitous in control and robotics. In classical paradigms, the controller is designed first and then analysis will be carried out to quantify the effects of the uncertainty (uncertainty quantification). The goal of this project is to incorporate uncertainty directly in the controller synthesis step so as to reduce the number of design iterations required to achieve certain performance. This follows the line of our earlier work on covariance control.

• Optimal Mass Transport: Another stream of my research is on optimal mass transport (OMT). We have developed multiple algorithms and extended OMT theory from several perspectives during the last five years. I plan to continue this exciting line of research and further explore its applications in machine learning and control.