R-SPIDER: A Fast Riemannian Stochastic Optimization Algorithm with Curvature Independent Rate

We study smooth stochastic optimization problems on Riemannian manifolds. Via adapting the recently proposed SPIDER algorithm citepfang2018spider (a variance reduced stochastic method) to Riemannian manifold, we can achieve faster rate than known algorithms in both the finite sum and stochastic settings. Unlike previous works, by not resorting to bounding iterate distances, our analysis yields curvature independent convergence rates for both the nonconvex and strongly convex cases.