Recent Advances in Stochastic Riemannian Optimization

Reshad Hosseini () and Suvrit Sra ()
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Reshad Hosseini: University of Tehran, School of ECE, College of Engineering
Suvrit Sra: Massachusetts Institute of Technology

Chapter Chapter 19 in Handbook of Variational Methods for Nonlinear Geometric Data, 2020, pp 527-554 from Springer

Abstract: Abstract Stochastic and finite-sum optimization problems are central to machine learning. Numerous specializations of these problems involve nonlinear constraints where the parameters of interest lie on a manifold. Consequently, stochastic manifold optimization algorithms have recently witnessed rapid growth, also in part due to their computational performance. This chapter outlines numerous stochastic optimization algorithms on manifolds, ranging from the basic stochastic gradient method to more advanced variance reduced stochastic methods. In particular, we present a unified summary of convergence results. Finally, we also provide several basic examples of these methods to machine learning problems, including learning parameters of Gaussians mixtures, principal component analysis, and Wasserstein barycenters.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-31351-7_19

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DOI: 10.1007/978-3-030-31351-7_19

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