Speaker: Mohammad Farazmand
Affiliation: NC State University
Title: Multiscale analysis of accelerated gradient methods
Abstract: Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow. Using geometric singular perturbation theory, we show that, under certain conditions, the accelerated gradient flow possesses an attracting invariant slow manifold to which the trajectories of the flow converge asymptotically. We obtain a general explicit expression in the form of functional series expansions that approximates the slow manifold to any arbitrary order of accuracy. To the leading order, the accelerated gradient flow reduced to this slow manifold coincides with the usual gradient descent. We illustrate the implications of our results on three examples.
Wednesday, September 16 at 4:45pm to 5:45pm
Ayres Hall, 112
1403 Circle Drive, Knoxville, TN 37996