STOR Colloquium: Rong Ge, Duke University
Optimization Landscape for Matrix Completion
Matrix completion is a popular approach for recommendation systems. In theory, it can be solved using complicated convex relaxations, while in practice even simple algorithms such as stochastic gradient descent can always converge to the optimal solution. In this talk we will see some new results on the optimization landscape for the natural non-convex objective of matrix completion. In particular, we will show that although the natural objective is non-convex and has many saddle points, all of its local minima are equivalent to the global optimal solution. We will also discuss why such properties allow simple algorithms such as stochastic gradient descent to converge efficiently from an arbitrary initial point.
Refreshments will be served at 3:00pm in the 3rd floor lounge of Hanes Hall