Convergence of Riemannian Stochastic Gradient Descents: Varying Batch Sizes And Nonstandard Batch Forming
Optimization and Control
2026-04-21 v3
Abstract
We establish convergence theorems for Riemannian stochastic gradient descents in which the underlying probability spaces vary from iteration to iteration. As applications, we deduce convergence results for Riemannian stochastic gradient descents with varying batch sizes and unbiased batch forming schemes.
Keywords
Cite
@article{arxiv.2604.06350,
title = {Convergence of Riemannian Stochastic Gradient Descents: Varying Batch Sizes And Nonstandard Batch Forming},
author = {Hao Wu},
journal= {arXiv preprint arXiv:2604.06350},
year = {2026}
}
Comments
17 pages. Version 2: strengthened assumptions to make proofs rigorous, corrected typos. Version 3: refined measurability assumptions, updated proofs, added mean square convergence to Theorem 2.4