The Dynamics of Riemannian Robbins-Monro Algorithms. (arXiv:2206.06795v2 [math.OC] UPDATED)

Many important learning algorithms, such as stochastic gradient methods, are
often deployed to solve nonlinear problems on Riemannian manifolds. Motivated
by these applications, we propose a family of Riemannian algorithms
generalizing and extending the seminal stochastic approximation framework of
Robbins and Monro. Compared to their Euclidean counterparts, Riemannian
iterative algorithms are much less understood due to the lack of a global
linear structure on the manifold. We overcome this difficulty by introducing an
extended Fermi coordinate frame which allows us …

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