We give quantitative estimates for the rate of convergence of Riemannian stochastic
gradient descent (RSGD) to Riemannian gradient flow and to a diffusion process, the so …

In this paper, we examine the long-run distribution of stochastic gradient descent (SGD) in
general, non-convex problems. Specifically, we seek to understand which regions of the …

Global optimization is critical in engineering, computer science, and various industrial
applications as it aims to find optimal solutions for complex problems. The development of …

Non-convex minimization problems are universally considered hard, and even guaranteeing
that a computed solution is locally minimizing is known to be NP-hard. In this general …

Real-world datasets often exhibit a long-tailed distribution, where vast majority of classes
known as tail classes have only few samples. Traditional methods tend to overfit on these …

Stochastic approximation methods are a class of iterative algorithms that play an essential
role in applications involving noisy and incomplete observations. Rooted in the seminal …