Stochastic Approximation on Riemannian manifolds
Optimization and Control
2017-11-30 v1
Abstract
The standard theory of stochastic approximation (SA) is extended to the case when the constraint set is a Riemannian manifold. Specifically, the standard ODE method for analyzing SA schemes is extended to iterations constrained to stay on a manifold using a retraction mapping. In addition, for submanifolds of a Euclidean space, a framework is developed for a projected SA scheme with approximate retractions. The framework is also extended to non-differentiable constraint sets.
Cite
@article{arxiv.1711.10754,
title = {Stochastic Approximation on Riemannian manifolds},
author = {Suhail M. Shah},
journal= {arXiv preprint arXiv:1711.10754},
year = {2017}
}
Comments
28 pages, 1 Figure