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Stochastic Variance-Reduced Cubic regularization (SVRC) algorithms have received increasing attention due to its improved gradient/Hessian complexities (i.e., number of queries to stochastic gradient/Hessian oracles) to find local minima for nonconvex finite-sum optimization.
Optimal finite-sum smooth non-convex optimization with sarah
Nguyen, L. M · 1901
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Sharp analysis for nonconvex sgd escaping from saddle points
Fang, C · 1902
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Stochastic gradient descent escapes saddle points efficiently
Jin, C · 1902
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A stochastic trust region method for non-convex minimization
Shen, Z · 1903
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Optimum bounds for the distributions of martingales in banach spaces
Pinelis, I · 1994
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Golub, G. H · 1996
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Trust region methods
Conn, A. R · 2000
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Cubic regularization of newton method and its global performance
Nesterov, Y · 2006
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Trust-region and other regularisations of linear least-squares problems
Cartis, C · 2009
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Libsvm: a library for support vector machines
Chang, C.-C · 2011
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Complexity bounds for second-order optimality in unconstrained optimization
Cartis, C · 2012
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A stochastic gradient method with an exponential convergence _rate for finite training sets
Roux, N. L · 2012
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User-friendly tail bounds for sums of random matrices
Tropp, J. A · 2012
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On the evaluation complexity of cubic regularization methods for potentially rank-deficient nonlinear least-squares problems and its relevance to constrained nonlinear optimization
Cartis, C · 2013
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Most tensor problems are np-hard
Hillar, C. J · 2013
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Accelerating stochastic gradient descent using predictive variance reduction
Johnson, R · 2013
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Saga: A fast incremental gradient method with support for non-strongly convex composite objectives
Defazio, A · 2014
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Fast and simple pca via convex optimization
Garber, D · 2015
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Escaping from saddle points—online stochastic gradient for tensor decomposition
Ge, R · 2015
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Deep learning
LeCun, Y · 2015
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Variance reduction for faster non-convex optimization
Allen-Zhu, Z · 2016
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Global optimality of local search for low rank matrix recovery
Bhojanapalli, S · 2016
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Sub-sampled cubic regularization for non-convex optimization
Kohler, J. M · 2017
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Cubic-regularization counterpart of a variable-norm trust-region method for unconstrained minimization
Martínez, J. M · 2017
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Sarah: A novel method for machine learning problems using stochastic recursive gradient
Nguyen, L. M · 2017
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Complexity analysis of second-order line-search algorithms for smooth nonconvex optimization
Royer, C. W · 2017
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Newton-type methods for non-convex optimization under inexact hessian information
Xu, P · 2017
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Convergence rate analysis of a stochastic trust region method for nonconvex optimization
Blanchet, J · 2016
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Gradient descent efficiently finds the cubic-regularized non-convex newton step
Carmon, Y · 2016
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Matrix completion has no spurious local minimum
Ge, R · 2016
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Identity matters in deep learning
Hardt, M · 2016
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Deep learning without poor local minima
Kawaguchi, K · 2016
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Stochastic variance reduction for nonconvex optimization 314–323
Reddi, S. J · 2016
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Saving gradient and negative curvature computations: Finding local minima more efficiently
Yu, Y · 2017
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Natasha 2: Faster non-convex optimization than sgd
Allen-Zhu, Z · 2018
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Neon2: Finding local minima via first-order oracles
Allen-Zhu, Z · 2018
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Analysis of krylov subspace solutions of regularized non-convex quadratic problems
Carmon, Y · 2018
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Accelerated methods for nonconvex optimization
Carmon, Y · 2018
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Spider: Near-optimal non-convex optimization via stochastic path integrated differential estimator
Fang, C · 2018
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Stochastic cubic regularization for fast nonconvex optimization
Tripuraneni, N · 2018
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First-order stochastic algorithms for escaping from saddle points in almost linear time
Xu, Y · 2018
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Third-order smoothness helps: faster stochastic optimization algorithms for finding local minima
Yu, Y · 2018
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Stochastic variance-reduced cubic regularization methods
Zhou, D · 2019
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A proximal stochastic gradient method with progressive variance reduction
Xiao, L · 2075
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