Variance reduction is popular in accelerating gradient descent and stochastic gradient
descent for optimization problems defined on both euclidean space and Riemannian …

This paper studies large-scale optimization problems on Riemannian manifolds whose
objective function is a finite sum of negative log-probability losses. Such problems arise in …

This work considers optimization of composition of functions in a nested form over
Riemannian manifolds where each function contains an expectation. This type of problems …

List of Figures 1.1 (1.1 a) 2-dimensional Poincaré disk model of hyperbolic geometry, which
is well-suited for embedding relational data with hierarchies.(1.1 b) Grassmann geometry …

Optimization methods have been extensively studied given their broad applications in areas
such as applied mathematics, statistics, engineering, healthcare, business, and finance. In …

In control and machine learning, the primary goal is to learn the models that make
predictions or decisions and act in the world. This thesis covers two important aspects for …