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Stochastic approximation (SA) is a classical approach for stochastic convex optimization.
Empirical risk minimization for stochastic convex optimization: O ( 1 / n ) {O}(1/n) - and O ( 1 / n 2 ) {O}(1/n^{2}) -type of risk bounds
Lijun Zhang, Tianbao Yang, and Rong Jin · 1979
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Problem Complexity and Method Efficiency in Optimization
A. Nemirovski and D. B. Yudin · 1983
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Incremental gradient algorithms with stepsizes bounded away from zero
M.V. Solodov · 1998
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Statistical Learning Theory
Vladimir N. Vapnik · 1998
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Stochastic Approximation and Recursive Algorithms and Applications
Harold J. Kushner and G. George Yin · 2003
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Convex Optimization
Stephen Boyd and Lieven Vandenberghe · 2004
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Solving large scale linear prediction problems using stochastic gradient descent algorithms
Tong Zhang · 2004
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Logarithmic regret algorithms for online convex optimization
Elad Hazan, Amit Agarwal, and Satyen Kale · 2007
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Concentration-of-measure inequalities
Gábor Lugosi · 2009
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Robust stochastic approximation approach to stochastic programming
A. Nemirovski, A. Juditsky, G. Lan, and A. Shapiro · 2009
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Stochastic convex optimization
Shai Shalev-Shwartz, Ohad Shamir, Nathan Srebro, and Karthik Sridharan · 2009
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Optimistic rates for learning with a smooth loss
Nathan Srebro, Karthik Sridharan, and Ambuj Tewari · 2010
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Adaptive subgradient methods for online learning and stochastic optimization
John Duchi, Elad Hazan, and Yoram Singer · 2011
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Beyond the regret minimization barrier: an optimal algorithm for stochastic strongly-convex optimization
Elad Hazan and Satyen Kale · 2011
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Non-asymptotic analysis of stochastic approximation algorithms for machine learning
Eric Moulines and Francis R. Bach · 2011
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Random gradient-free minimization of convex functions
Yurii Nesterov · 2011
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Information-theoretic lower bounds on the oracle complexity of stochastic convex optimization
Alekh Agarwal, Peter L. Bartlett, Pradeep Ravikumar, and Martin J. Wainwright · 2012
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Optimal stochastic approximation algorithms for strongly convex stochastic composite optimization i: A generic algorithmic framework
Saeed Ghadimi and Guanghui Lan · 2012
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Making gradient descent optimal for strongly convex stochastic optimization
Alexander Rakhlin, Ohad Shamir, and Karthik Sridharan · 2012
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Stochastic gradient descent, weighted sampling, and the randomized kaczmarz algorithm
Deanna Needell, Rachel Ward, and Nati Srebro · 2014
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Lectures on Stochastic Programming: Modeling and Theory
Alexander Shapiro, Darinka Dentcheva, and Andrzej Ruszczyński · 2014
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Online convex programming and generalized infinitesimal gradient ascent
Martin Zinkevich · 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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A Guide to Sample Average Approximation , pages 207–243
Sujin Kim, Raghu Pasupathy, and Shane G. Henderson · 2015
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Fast rates for exp-concave empirical risk minimization
Tomer Koren and Kfir Levy · 2015
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Nicolas Le Roux, Mark Schmidt, and Francis Bach · 2012
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Finite sample convergence rates of zero-order stochastic optimization methods
Andre Wibisono, Martin J Wainwright, Michael I. Jordan, and John C. Duchi · 2012
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Non-strongly-convex smooth stochastic approximation with convergence rate O ( 1 / n ) {O}(1/n)
Francis Bach and Eric Moulines · 2013
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Fast convergence of stochastic gradient descent under a strong growth condition
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Stochastic dual coordinate ascent methods for regularized loss minimization
Shai Shalev-Shwartz and Tong Zhang · 2013
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Lower and upper bounds on the generalization of stochastic exponentially concave optimization
Mehrdad Mahdavi, Lijun Zhang, and Rong Jin · 2015
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Variance reduction for faster non-convex optimization
Zeyuan Allen-Zhu and Elad Hazan · 2016
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Generalization of ERM in stochastic convex optimization: The dimension strikes back
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Fast rates with high probability in exp-concave statistical learning
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Stochastic variance reduction for nonconvex optimization
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Memory and communication efficient distributed stochastic optimization with minibatch prox
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A hitting time analysis of stochastic gradient langevin dynamics
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