Riemannian随机梯度下降的收敛性：可变批量大小与非标准批量形成
最优化与控制
2026-04-21 v3
摘要
我们在迭代之间变化的概率空间上建立了Riemannian随机梯度下降的收敛定理。作为应用，我们推导出具有可变批量大小和无偏批量形成方案的Riemannian随机梯度下降的收敛结果。
引用
@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}
}
备注
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