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

arXiv: https://arxiv.org/abs/1811.04194 · HTML: https://mlsanity.com/paper/1811.04194/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Nov 2018.

## Built on by (most cited first, 4 of 4)

- [Low-complexity subspace-descent over symmetric positive definite manifold](https://mlsanity.com/paper/2305.02041/) (2023)
- [Streamlining in the Riemannian Realm: Efficient Riemannian Optimization with Loopless Variance Reduction](https://mlsanity.com/paper/2403.06677/) (2024)
- [Continuous-time Riemannian SGD and SVRG Flows on Wasserstein Probabilistic Space](https://mlsanity.com/paper/2401.13530/) (2024)
- [Fr'echet Regression on the Bures-Wasserstein Manifold](https://mlsanity.com/paper/2604.03566/) (2026)

## Abstract (arXiv)

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.