Yuetian Luo is working with Anru Zhang (Statistics) and Yingyu Liang (Computer Science) on non-convex optimization problems involving low rank matrices and implicit regularization for non-convex optimization methods. We develop novel fast algorithms with provable faster convergence guarantees than common first order methods. The algorithm is based on a new sketching scheme we developed for high dimensional problems. Also we are interested in investigating implicit regularization for different non-convex optimization methods and different initialization schemes.
