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.
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.
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.
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