# Stochastic Approximation on Riemannian manifolds

arXiv: https://arxiv.org/abs/1711.10754 · HTML: https://mlsanity.com/paper/1711.10754/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2017.

## Built on by (most cited first, 7 of 7)

- [EigenGame Unloaded: When playing games is better than optimizing](https://mlsanity.com/paper/2102.04152/) (2021)
- [Riemannian stochastic approximation algorithms](https://mlsanity.com/paper/2206.06795/) (2022)
- [Stochastic Modified Flows for Riemannian Stochastic Gradient Descent](https://mlsanity.com/paper/2402.03467/) (2024)
- [The Symmetric Generalized Eigenvalue Problem as a Nash Equilibrium](https://mlsanity.com/paper/2206.04993/) (2022)
- [A Generalized EigenGame with Extensions to Multiview Representation Learning](https://mlsanity.com/paper/2211.11323/) (2022)
- [Tame Riemannian Stochastic Approximation](https://mlsanity.com/paper/2302.00709/) (2023)
- [Stochastic gradient descent with discontinuity across a manifold](https://mlsanity.com/paper/2608.07618/) (2026)

## Abstract (arXiv)

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.