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Accelerated Stochastic Quasi-Newton Optimization on Riemann Manifolds

Abstract · Apr 6, 2017 03:34 ·

math-oc math-dg stat-ml

Arxiv Abstract

  • Anirban Roychowdhury
  • Srinivasan Parthasarathy

We propose L-BFGS and trust-region algorithms on Riemann manifolds that use stochastic variance reduction techniques to speed up convergence. For the stochastic L-BFGS algorithm we analyze and prove linear convergence rates for geodesically convex problems on the manifold, without resorting to linesearch methods designed to satisfy Wolfe conditions on the step size. To the best of our knowledge our trust-region method with stochastic variance reduction techniques is the first of its kind in the literature. We conduct experiments on Karcher mean computation for positive definite matrices and computation of leading eigenvectors for both synthetic and real data matrices, and demonstrate notably better performance than recently-proposed first-order stochastic optimization methods on Riemann manifolds, as well as standard trust-region manifold optimization techniques.

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