Learning Regularizers - Bilevel Optimization or Unrolling

Abstract

In this talk the speaker will consider the problem of learning a convex regularizer from a theoretical perspective. In general, learning of variational methods can be done by bilevel optimization where the variational problem is the lower level problem and the upper level problem minimizes over some parameter of the lower level problem. However, this is usually too difficult in practice and one practically feasible method is the approach by so-called unrolling (or unfolding). Therefore, one replaces the lower level problem by an algorithm that converges to a solution of that problem and uses the N-th iterate instead of the true solution. While this approach is often successful in practice little theoretical results are available. In this talk the speaker will consider a situation in which one can make a thorough comparison of the bilevel approach and the unrolling approach in a particular case of a quite simple toy example. Even though the example is quite simple, the situation is already quite complex and reveals a few phenomena that have been observed in practice.

For Attendees' Attention

This talk is hosted by the Department of Mathematics of the Chinese University of Hong Kong and will be held online via Zoom. To attend, please join the Zoom meeting at https://cuhk.zoom.us/j/98241093146 (Meeting ID: 982 4109 3146).

About the Program

For more information, please refer to the program website at https://iasprogram.hkust.edu.hk/inverseproblems/.