Reviews: Riemannian SVRG: Fast Stochastic Optimization on Riemannian Manifolds

This paper addresses a topic that was proposed as future work in [32], and by design, much of its contents are adaptations of results found in [14] and [21]. Thus, the analysis is incremental. Nonetheless, the paper contributes a manifoldized algorithm and bridges a gap between convex optimization and Riemannian optimization. Furthermore, the paper provides a useful lemma to analyze Riemannian methods, which can have a lasting impact. My main concern with this paper is its presentation.