An accelerated first-order method for non-convex optimization on manifolds

Understand

We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case.

• Under Lipschitz assumptions on the Riemannian gradient and Hessian of the cost function, these methods find approximate first-order critical points faster than regular gradient descent.
• A randomized version also finds approximate second-order critical points.
• Both the algorithms and their analyses build extensively on existing work in the Euclidean case.