The paper develops an inversion-free natural gradient descent algorithm on Riemannian manifolds that maintains an online approximation of the inverse Fisher information matrix using transported score vectors and proves almost-sure convergence rates of O(log s / s^α) for α > 2/3.
Takatsu (2011), Malagò et al
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Inversion-Free Natural Gradient Descent on Riemannian Manifolds
The paper develops an inversion-free natural gradient descent algorithm on Riemannian manifolds that maintains an online approximation of the inverse Fisher information matrix using transported score vectors and proves almost-sure convergence rates of O(log s / s^α) for α > 2/3.