Convergence of Riemannian Stochastic Gradient Descents: Varying Batch Sizes And Nonstandard Batch Forming

TL;DR

This paper proves convergence theorems for Riemannian stochastic gradient descent algorithms with changing probability spaces, batch sizes, and batch forming schemes.

Contribution

It introduces convergence results for Riemannian stochastic gradient descent with varying batch sizes and nonstandard batch forming.

Findings

Established convergence theorems for Riemannian stochastic gradient descent.

Applied results to schemes with varying batch sizes and unbiased batch forming.

Provided theoretical guarantees under changing probability spaces.

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.