Riemannian Stochastic Variance Reduced Gradient Algorithm with Retraction and Vector Transport

DOI10.1137/17M1116787zbMath1421.90084arXiv1702.05594WikidataQ115246947 ScholiaQ115246947MaRDI QIDQ5231672

Hiroyuki Sato, Bamdev Mishra, Hiroyuki Kasai

Publication date: 27 August 2019

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.05594

zbMATH Keywords

matrix completionprincipal component analysisretractionRiemannian optimizationvector transportRiemannian centroidstochastic variance reduced gradient

Mathematics Subject Classification ID

Large-scale problems in mathematical programming (90C06) Nonlinear programming (90C30) Stochastic programming (90C15)

Related Items (21)

Some Limit Properties of Markov Chains Induced by Recursive Stochastic Algorithms ⋮ Riemannian Conjugate Gradient Methods: General Framework and Specific Algorithms with Convergence Analyses ⋮ Measure estimation on manifolds: an optimal transport approach ⋮ Riemannian stochastic fixed point optimization algorithm ⋮ Sequential Quadratic Optimization for Nonlinear Optimization Problems on Riemannian Manifolds ⋮ Optimizing Oblique Projections for Nonlinear Systems using Trajectories ⋮ An efficient damped Newton-type algorithm with globalization strategy on Riemannian manifolds ⋮ Riemannian smoothing gradient type algorithms for nonsmooth optimization problem on compact Riemannian submanifold embedded in Euclidean space ⋮ Sion’s Minimax Theorem in Geodesic Metric Spaces and a Riemannian Extragradient Algorithm ⋮ Riemannian stochastic variance-reduced cubic regularized Newton method for submanifold optimization ⋮ Riemannian Hamiltonian Methods for Min-Max Optimization on Manifolds ⋮ Riemannian optimization on unit sphere with \(p\)-norm and its applications ⋮ A variance-reduced stochastic gradient tracking algorithm for decentralized optimization with orthogonality constraints ⋮ Riemannian Natural Gradient Methods ⋮ A brief introduction to manifold optimization ⋮ Cayley-transform-based gradient and conjugate gradient algorithms on Grassmann manifolds ⋮ Geometric Methods on Low-Rank Matrix and Tensor Manifolds ⋮ Recent Advances in Stochastic Riemannian Optimization ⋮ Riemannian conjugate gradient methods with inverse retraction ⋮ A Riemannian gossip approach to subspace learning on Grassmann manifold ⋮ Sequential optimality conditions for nonlinear optimization on Riemannian manifolds and a globally convergent augmented Lagrangian method

Uses Software

• Manopt
• Eigentaste
• Saga

Cites Work

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• Low-rank tensor completion by Riemannian optimization
• A Riemannian symmetric rank-one trust-region method
• A survey and comparison of contemporary algorithms for computing the matrix geometric mean
• A Riemannian framework for tensor computing
• Riemannian Preconditioning
• Manopt, a Matlab toolbox for optimization on manifolds
• A Broyden Class of Quasi-Newton Methods for Riemannian Optimization
• A Proximal Stochastic Gradient Method with Progressive Variance Reduction
• Incremental Majorization-Minimization Optimization with Application to Large-Scale Machine Learning
• Quasi-Martingales
• Stochastic Gradient Descent on Riemannian Manifolds
• Stochastic Dual Coordinate Ascent Methods for Regularized Loss Minimization

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