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Cubic regularization (CR) is an optimization method with emerging popularity due to its capability to escape saddle points and converge to second-order stationary solutions for nonconvex optimization.
Sub-sampled cubic regularization for non-convex optimization
Kohler, J. M. and Lucchi, A. (2017) · 1904
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Probability inequalities for sums of bounded random variables
Hoeffding, W. (1963) · 1963
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Neural networks and principal component analysis: Learning from examples without local minima
Baldi, P. and Hornik, K. (1989) · 1989
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Cubic regularization of newton’s method and its global performance
Nesterov, Y. and Polyak, B. (2006) · 2006
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Positive Definite Matrices
Bhatia, R. (2007) · 2007
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Accelerating the cubic regularization of newton’s method on convex problems
Nesterov, Y. (2008) · 2008
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Robust stochastic approximation approach to stochastic programming
Nemirovski, A. S., Juditsky, A., Lan, G., and Shapiro, A. (2009) · 2009
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Adaptive cubic regularization methods for unconstrained optimization. part i : motivation, convergence and numerical results
Cartis, C., Gould, N. I. M., and Toint, P. L. (2011) · 2011
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Hybrid deterministic-stochastic methods for data fitting
Friedlander, M. and Schmidt, M. (2012) · 2012
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An optimal method for stochastic composite optimization
Lan, G. (2012) · 2012
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Toward a noncommutative arithmetic-geometric mean inequality: conjectures, case-studies, and consequences
Recht, B. and Re, C. (2012) · 2012
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User-friendly tail bounds for sums of random matrices
Tropp, J. A. (2012) · 2012
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Accelerating stochastic gradient descent using predictive variance reduction
Johnson, R. and Zhang, T. (2013) · 2013
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Concentration inequalities for sampling without replacement
Bardenet, R. and Maillard, O. (2015) · 2015
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Why Random Reshuffling Beats Stochastic Gradient Descent
Gürbüzbalaban, M., Ozdaglar, A., and Parrilo, P. (2015) · 2015
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Escaping from saddle points — online stochastic gradient for tensor decomposition
Rong, G.and Furong, H., Chi, J., and Yang, Y. (2015) · 2015
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Global optimality of local search for low rank matrix recovery
Bhojanapalli, S., Neyshabur, B., and Srebro, N. (2016) · 2016
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Gradient descent efficiently finds the cubic-regularized non-convex Newton step
Carmon, Y. and Duchi, J. C. (2016) · 2016
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How to escape saddle points efficiently
Chi, J., Rong, G., Praneeth, N., K., S. M., and Michael, I. J. (2017) · 2017
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Second-order methods with cubic regularization under inexact information
Ghadimi, S., Liu, H., and Zhang, T. (2017) · 2017
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Jiang, B., Lin, T., and Zhang, S. (2017) · 2017
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On noisy negative curvature descent: competing with gradient descent for faster non-convex optimization
Liu, M. and Yang, T. (2017) · 2017
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A geometrical analysis of phase retrieval
Sun, J., Qu, Q., and Wright, J. (2017) · 2017
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Stochastic Cubic Regularization for Fast Nonconvex Optimization
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Carmon, Y., Duchi, J. C., Hinder, O., and Sidford, A. (2016) · 2016
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Matrix completion has no spurious local minimum
Ge, R., Lee, J., and Ma, T. (2016) · 2016
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Accelerated gradient methods for nonconvex nonlinear and stochastic programming
Ghadimi, S. and Lan, G. (2016) · 2016
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Gradient descent only converges to minimizers
Lee, J. D., Simchowitz, M., Jordan, M. I., and Recht, B. (2016) · 2016
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Stochastic variance reduction for nonconvex optimization
Reddi, S., Hefny, A., Sra, S., B., P., and A., S. (2016) · 2016
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Without-replacement sampling for stochastic gradient methods
Shamir, O. (2016) · 2016
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Finding approximate local minima faster than gradient descent
Agarwal, N., Allen-Zhu, Z., Bullins, B., Hazan, E., and Ma, T. (2017) · 2017
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Tripuraneni, N., Stern, M., Jin, C., Regier, J., and Jordan, M. I. (2017) · 2017
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Newton-type methods for non-convex optimization under inexact hessian information
Xu, P., Roosta-Khorasani, F., and Mahoney, M. W. (2017) · 2017
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NEON+: Accelerated gradient methods for extracting negative curvature for non-convex optimization
Xu, Y., Jin, R., and Yang, T. (2017) · 2017
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A Note on Inexact Condition for Cubic Regularized Newton’s Method
Wang, Z., Zhou, Y., Liang, Y., and Lan, G. (2018) · 2018
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Stochastic Variance-Reduced Cubic Regularized Newton Method
Zhou, D., Xu, P., and Gu, Q. (2018) · 2018
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Convergence of cubic regularization for nonconvex optimization under KL property
Zhou, Y., Wang, Z., and Liang, Y. (2018) · 2018
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A proximal stochastic gradient method with progressive variance reduction
Xiao, L. and Zhang, T. (2014) · 2075
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