Stochastic Approximation on Riemannian manifolds

Suhail M. Shah

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arXiv · 1711.10754

Stochastic Approximation on Riemannian manifolds

Suhail M. Shah

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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.

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Suhail M. Shah. 2017-11-29. Stochastic Approximation on Riemannian manifolds. https://arxiv.org/abs/1711.10754

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