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We analyze stochastic gradient algorithms for optimizing nonconvex problems.
Probability inequalities for sums of bounded random variables
Wassily Hoeffding · 1963
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Introductory Lectures on Convex Optimization: A Basic Course
Yurii Nesterov · 2004
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Concentration inequalities and martingale inequalities: a survey
Fan Chung and Linyuan Lu · 2006
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Cubic regularization of newton method and its global performance
Yurii Nesterov and Boris T Polyak · 2006
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User-friendly tail bounds for matrix martingales
Joel A Tropp · 2011
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User-friendly tail bounds for sums of random matrices
Joel A Tropp · 2012
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Accelerating stochastic gradient descent using predictive variance reduction
Rie Johnson and Tong Zhang · 2013
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Saga: A fast incremental gradient method with support for non-strongly convex composite objectives
Aaron Defazio, Francis Bach, and Simon Lacoste-Julien · 2014
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Escaping from saddle points — online stochastic gradient for tensor decomposition
Rong Ge, Furong Huang, Chi Jin, and Yang Yuan · 2015
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Random matrices: Universality of local spectral statistics of non-hermitian matrices
Terence Tao and Van Vu · 2015
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Finding approximate local minima for nonconvex optimization in linear time
Naman Agarwal, Zeyuan Allen-Zhu, Brian Bullins, Elad Hazan, and Tengyu Ma · 2016
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Variance reduction for faster non-convex optimization
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Global optimality of local search for low rank matrix recovery
Srinadh Bhojanapalli, Behnam Neyshabur, and Nati Srebro · 2016
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Accelerated methods for non-convex optimization
Yair Carmon, John C Duchi, Oliver Hinder, and Aaron Sidford · 2016
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Matrix completion has no spurious local minimum
Rong Ge, Jason D Lee, and Tengyu Ma · 2016
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Mini-batch stochastic approximation methods for nonconvex stochastic composite optimization
Saeed Ghadimi, Guanghui Lan, and Hongchao Zhang · 2016
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Stochastic variance reduction for nonconvex optimization
Sarah: A novel method for machine learning problems using stochastic recursive gradient
Lam M Nguyen, Jie Liu, Katya Scheinberg, and Martin Takáč · 2017
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Natasha 2: Faster non-convex optimization than sgd
Zeyuan Allen-Zhu · 2018
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Neon2: Finding local minima via first-order oracles
Zeyuan Allen-Zhu and Yuanzhi Li · 2018
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Escaping saddles with stochastic gradients
Hadi Daneshmand, Jonas Kohler, Aurelien Lucchi, and Thomas Hofmann · 2018
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Spider: Near-optimal non-convex optimization via stochastic path-integrated differential estimator
Cong Fang, Chris Junchi Li, Zhouchen Lin, and Tong Zhang · 2018
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Gradient descent can take exponential time to escape saddle points
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Finding local minima via stochastic nested variance reduction
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Stochastic nested variance reduction for nonconvex optimization
Dongruo Zhou, Pan Xu, and Quanquan Gu
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First-order stochastic algorithms for escaping from saddle points in almost linear time
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Stabilized svrg: Simple variance reduction for nonconvex optimization
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Proxsarah: An efficient algorithmic framework for stochastic composite nonconvex optimization
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