Inexact Trust-region Algorithms On Riemannian Manifolds

Authors:
Hiroyuki Kasai The University of Electro-Communications
Bamdev Mishra Microsoft

Introduction:

The authors consider an inexact variant of the popular Riemannian trust-region algorithm for structured big-data minimization problems.The proposed algorithm approximates the gradient and the Hessian in addition to the solution of a trust-region sub-problem.

Abstract:

We consider an inexact variant of the popular Riemannian trust-region algorithm for structured big-data minimization problems. The proposed algorithm approximates the gradient and the Hessian in addition to the solution of a trust-region sub-problem. Addressing large-scale finite-sum problems, we specifically propose sub-sampled algorithms with a fixed bound on sub-sampled Hessian and gradient sizes, where the gradient and Hessian are computed by a random sampling technique. Numerical evaluations demonstrate that the proposed algorithms outperform state-of-the-art Riemannian deterministic and stochastic gradient algorithms across different applications.

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