Dr. Martin J. Mohlenkamp
The Dynamical Systems and Mathematical Biology Seminar presents Dr. Martin Mohlenkamp discussing “Transient Dynamics of Block Coordinate Descent in a Valley” on Tuesday, Nov. 6, from 3:05 to 4 p.m., in Morton 313.
Mohlenkamp is Associate Professor of Mathematics at Ohio University.
Abstract: Block Coordinate Descent algorithms for optimization have appealing features, most notably the relative ease of solving the block optimization problem at each step. However, they can also perform poorly, especially when they encounter a valley in the optimization landscape.
We show that iterates converge linearly to a vicinity of the valley floor and then progress in a zig-zag fashion along the direction of the valley floor. Progress along the direction of the valley floor is proportional to the gradient on the valley floor and inversely proportional to the “narrowness” of the valley. Progress also depends on the direction of the valley with respect to the blocks of coordinates. We show that in higher dimensions nearly all directions give progress similar to the worst case direction.
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