Research Interests

Interests

My research interests lie at the intersection of control, machine learning and robotics. Below are several research topics we are currently looking into.

• Markov Chain Monte Carlo: Markov chain Monte Carlo (MCMC) is a powerful tool used for sampling from given probability distributions, enabling statistical inference and uncertainty quantification in a wide range of applications. Unlike optimization approaches that yield point estimates, MCMC sampling methods offer the advantage of quantifying uncertainties and confidence intervals of these estimates using samples. Compared with optimization, the development of MCMC is still in its early stage. We aim to develop faster MCMC algorithms with a performance guarantee. Our proximal sampler in ‘‘Improved dimension dependence of a proximal algorithm for sampling’’ stands as the most efficient MCMC algorithm to date.

• Generative AI: Generative AI tools such as ChatGPT and Midjourney that create new images or text have shocked the public with their incredible performance. We are interested in understanding the mathematical principles of these tools and developing more efficient algorithms for generative AI. The specific generative AI we have been focusing on is the diffusion model. Our algorithm DEIS: Diffusion Exponential Integrator Sampler in ‘‘Fast Sampling of Diffusion Models with Exponential Integrator’’ is currently one of the most efficient training-free inference algorithms from a diffusion model.

• 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 stochastic control and covariance control.

• 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.

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

• 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.