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We consider the minimization of non-convex functions that typically arise in machine learning.
Trust region methods
Conn, Andrew R, Gould, Nicholas IM, and Toint, Philippe L · 2000
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Introductory lectures on convex optimization. applied optimization, vol. 87, 2004
Nesterov, Yurii · 2004
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Cubic regularization of newton method and its global performance
Nesterov, Yurii and Polyak, Boris T · 2006
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Learning multiple layers of features from tiny images
Krizhevsky, Alex and Hinton, Geoffrey · 2009
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On the use of stochastic hessian information in optimization methods for machine learning
Byrd, Richard H, Chin, Gillian M, Neveitt, Will, and Nocedal, Jorge · 2011
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Libsvm: a library for support vector machines
Chang, Chih-Chung and Lin, Chih-Jen · 2011
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Recovering low-rank matrices from few coefficients in any basis
Gross, David · 2011
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Hybrid deterministic-stochastic methods for data fitting
Friedlander, Michael P and Schmidt, Mark · 2012
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Updating the regularization parameter in the adaptive cubic regularization algorithm
Gould, Nicholas IM, Porcelli, M, and Toint, Philippe L · 2012
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A stochastic gradient method with an exponential convergence rate for finite training sets
Roux, Nicolas L, Schmidt, Mark, and Bach, Francis R · 2012
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Stochastic first-and zeroth-order methods for nonconvex stochastic programming
Ghadimi, Saeed and Lan, Guanghui · 2013
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Most tensor problems are np-hard
Hillar, Christopher J and Lim, Lek-Heng · 2013
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Accelerating stochastic gradient descent using predictive variance reduction
Johnson, Rie and Zhang, Tong · 2013
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Identifying and attacking the saddle point problem in high-dimensional non-convex optimization
Dauphin, Yann N, Pascanu, Razvan, Gulcehre, Caglar, Cho, Kyunghyun, Ganguli, Surya, and Bengio, Yoshua · 2014
Cited alongside, same era.
Saga: A fast incremental gradient method with support for non-strongly convex composite objectives
Variance reduced stochastic gradient descent with neighbors
Hofmann, Thomas, Lucchi, Aurelien, Lacoste-Julien, Simon, and McWilliams, Brian · 2015
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When are nonconvex problems not scary?
Sun, Ju, Qu, Qing, and Wright, John · 2015
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Finding local minima for nonconvex optimization in linear time
Agarwal, Naman, Allen-Zhu, Zeyuan, Bullins, Brian, Hazan, Elad, and Ma, Tengyu · 2016
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Convergence rate analysis of a stochastic trust region method for nonconvex optimization
Blanchet, Jose, Cartis, Coralia, Menickelly, Matt, and Scheinberg, Katya · 2016
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Gradient descent efficiently finds the cubic-regularized non-convex newton step
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Defazio, Aaron, Bach, Francis, and Lacoste-Julien, Simon · 2014
Cited alongside, same era.
The loss surfaces of multilayer networks
Choromanska, Anna, Henaff, Mikael, Mathieu, Michael, Arous, Gérard Ben, and LeCun, Yann · 2015
Cited alongside, same era.
Convergence rates of sub-sampled newton methods
Erdogdu, Murat A and Montanari, Andrea · 2015
Cited alongside, same era.
Escaping from saddle points-online stochastic gradient for tensor decomposition
Ge, Rong, Huang, Furong, Jin, Chi, and Yuan, Yang · 2015
Cited alongside, same era.
Adaptive cubic regularisation methods for unconstrained optimization. part i: motivation, convergence and numerical results
Cartis, Coralia, Gould, Nicholas IM, and Toint, Philippe L
Cited in the paper.
Adaptive cubic regularisation methods for unconstrained optimization. part ii: worst-case function-and derivative-evaluation complexity
Cartis, Coralia, Gould, Nicholas IM, and Toint, Philippe L
Cited in the paper.
Stochastic variance reduction for nonconvex optimization
Reddi, Sashank J, Hefny, Ahmed, Sra, Suvrit, Poczos, Barnabas, and Smola, Alex
Cited in the paper.
Carmon, Yair and Duchi, John C · 2016
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Starting small - learning with adaptive sample sizes
Daneshmand, Hadi, Lucchi, Aurélien, and Hofmann, Thomas · 2016
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A linear-time algorithm for trust region problems
Hazan, Elad and Koren, Tomer · 2016
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Global convergence rate analysis of unconstrained optimization methods based on probabilistic models
Cartis, Coralia and Scheinberg, Katya · 2017
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