The Riemannian Langevin equation and conic programs
Probability
2023-02-24 v1
Abstract
Diffusion limits provide a framework for the asymptotic analysis of stochastic gradient descent (SGD) schemes used in machine learning. We consider an alternative framework, the Riemannian Langevin equation (RLE), that generalizes the classical paradigm of equilibration in R^n to a Riemannian manifold (M^n, g). The most subtle part of this equation is the description of Brownian motion on (M^n, g). Explicit formulas are presented for some fundamental cones.
Cite
@article{arxiv.2302.11653,
title = {The Riemannian Langevin equation and conic programs},
author = {Govind Menon and Tianmin Yu},
journal= {arXiv preprint arXiv:2302.11653},
year = {2023}
}