A Universal Proximal Framework for Optimization and Sampling

Optimization and sampling are two fundamental pillars of data science since they play central roles in all aspects of learning, inference, and generation from data. Modern data science brings challenging questions to the design and analysis of algorithms for optimization and sampling due to undesirable but natural properties of data, such as randomness, nonsmoothnees, nonconvexity, and high dimensionality. On the other hand, various efficient algorithms have been developed to handle those challenges, for example stochastic gradient descent and accelerated gradient descent in optimization, and unadjusted Langevin algorithm in sampling. A natural question is whether there is a systematic understanding of existing algorithms that also helps to design new ones. In this talk, I introduce a universal proximal framework that is the guiding principle underlying all aforementioned algorithms for optimization and sampling. I also present three concrete examples from my works that are instances of the framework and have achieved either optimal or the best known results in nonsmooth optimization, stochastic optimization, and sampling. The universal proximal framework is a powerful idea in data science and will lead to more fruitful results. Finally, I conclude the talk by pointing out a few interesting problems in data science that require novel techniques beyond the classical theory in optimization and sampling.

Bio:

Jiaming Liang is an assistant professor in the Goergen Institute for Data Science and the department of Computer Science at the University of Rochester. He was a postdoctoral researcher in Computer Science at Yale University. He obtained Ph.D. in Operations Research from Georgia Institute of Technology. His research interests broadly include optimization and algorithms for data science, such as convex and nonconvex optimization, nonsmooth optimization, stochastic optimization, and high-dimensional sampling.