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Stochastic convex optimization, where the objective is the expectation of a random convex function, is an important and widely used method with numerous applications in machine learning, statistics, operations research and other areas.
Extremum problems with inequalities as subsidiary conditions
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The perceptron: a probabilistic model for information storage and organization in the brain
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Partitions of mass-distributions and convex bodies by hyperplanes
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On convergence proofs on perceptrons
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On an algorithm for the minimization of convex functions
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Randomized response: A survey technique for eliminating evasive answer bias
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Conjugate Duality and Optimization
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The widths of certain finite dimensional sets and classes of smooth functions
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On Cezari’s convergence of the steepest descent method for approximating saddle point of convex-concave functions
A. Nemirovski and D. Yudin · 1978
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A method of solving a convex programming problem with convergence rate o (1/k2)
Y. Nesterov · 1983
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Problem Complexity and Method Efficiency in Optimization
A.S. Nemirovsky and D.B. Yudin · 1983
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Learning quickly when irrelevant attributes abound: a new linear-threshold algorithm
N. Littlestone · 1987
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Introduction to Optimization
B.T. Poljak · 1987
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Geometric Algorithms and Combinatorial Optimization
M. Grötschel, L. Lovász, and A. Schrijver · 1988
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Sampling and integration of near log-concave functions
David Applegate and Ravi Kannan · 1991
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Sharp uniform convexity and smoothness inequalities for trace norms
K. Ball, E. Carlen, and E.H. Lieb · 1994
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Weakly learning DNF and characterizing statistical query learning using Fourier analysis
A. Blum, M. Furst, J. Jackson, M. Kearns, Y. Mansour, and S. Rudich · 1994
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Learning linear threshold functions in the presence of classification noise
T. Bylander · 1994
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Efficient Methods in Convex Programming
A. Nemirovski · 1994
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Isoperimetric problems for convex bodies and a localization lemma
R. Kannan, L. Lovász, and M. Simonovits · 1995
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Rounding of polytopes in the real number model of computation
L. G. Khachiyan · 1996
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A polynomial time algorithm for learning noisy linear threshold functions
A. Blum, A. Frieze, R. Kannan, and S. Vempala · 1997
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General convergence results for linear discriminant updates
A. Grove, N. Littlestone, and D. Schuurmans · 1997
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Learning with restricted focus of attention
S. Ben-David and E. Dichterman · 1998
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Large margin classification using the Perceptron algorithm
Y. Freund and R. Schapire · 1998
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Efficient noise-tolerant learning from statistical queries
M. Kearns · 1998
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On pac learning using winnow, perceptron, and a perceptron-like algorithm
R. Servedio · 1999
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Candidate one-way functions based on expander graphs
Oded Goldreich · 2000
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Relations between average case complexity and approximation complexity
U. Feige · 2002
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A linear lower bound on the unbounded error probabilistic communication complexity
J. Forster · 2002
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Revealing information while preserving privacy
I. Dinur and K. Nissim · 2003
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Solving convex programs by random walks
D. Bertsimas and S. Vempala · 2004
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On the generalization ability of on-line learning algorithms
N. Cesa-Bianchi, A. Conconi, and C. Gentile · 2004
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Practical privacy: the SuLQ framework
A. Blum, C. Dwork, F. McSherry, and K. Nissim · 2005
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On a theory of learning with similarity functions
M.-F. Balcan and A. Blum · 2006
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Map-reduce for machine learning on multicore
C. Chu, S. Kim, Y. Lin, Y. Yu, G. Bradski, A. Ng, and K. Olukotun · 2006
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Calibrating noise to sensitivity in private data analysis
C. Dwork, F. McSherry, K. Nissim, and A. Smith · 2006
Cited alongside, same era.
Simulated annealing for convex optimization
A. T. Kalai and S. Vempala · 2006
Cited alongside, same era.
Fast algorithms for logconcave functions: Sampling, rounding, integration and optimization
L. Lovász and S. Vempala · 2006
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Hit-and-run from a corner
L. Lovász and S. Vempala · 2006
Cited alongside, same era.
OptiML: an implicitly parallel domainspecific language for machine learning
A. K. Sujeeth, H. Lee, K. J. Brown, H. Chafi, M. Wu, A. R. Atreya, K. Olukotun, T. Rompf, and M. Odersky · 2011
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Information-theoretic lower bounds on the oracle complexity of stochastic convex optimization
A. Agarwal, P.L. Bartlett, P.D. Ravikumar, and M.J. Wainwright · 2012
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Distributed learning, communication complexity and privacy
M.-F. Balcan, A. Blum, S. Fine, and Y. Mansour · 2012
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Linear vs. semidefinite extended formulations: Exponential separation and strong lower bounds
S. Fiorini, S. Massar, S. Pokutta, H.R. Tiwary, and R. de Wolf · 2012
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Statistical active learning algorithms
M.-F. Balcan and Vitaly Feldman · 2013
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Lectures on modern convex optimization
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Simulated annealing in convex bodies and an O * {}^{\mbox{*}} ( n 4 {}^{\mbox{4}} ) volume algorithm
L. Lovász and S. Vempala · 2006
Cited alongside, same era.
Evolvability
L. G. Valiant · 2006
Cited alongside, same era.
Unconditional lower bounds for learning intersections of halfspaces
A. Klivans and A. Sherstov · 2007
Cited alongside, same era.
The geometry of logconcave functions and sampling algorithms
L. Lovász and S. Vempala · 2007
Cited alongside, same era.
A characterization of strong learnability in the statistical query model
H. Simon · 2007
Cited alongside, same era.
Smooth optimization with approximate gradient
A. d’Aspremont · 2008
Cited alongside, same era.
A. Ben-Tal and A. Nemirovski · 2013
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First-order methods with inexact oracle: the strongly convex case
O. Devolder, F. Glineur, and Y. Nesterov · 2013
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Local privacy and statistical minimax rates
J. C. Duchi, M. I. Jordan, and M. J. Wainwright · 2013
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Statistical algorithms and a lower bound for detecting planted cliques
V. Feldman, E. Grigorescu, L. Reyzin, S. Vempala, and Y. Xiao · 2013
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Approximate loss minimization with heavy tails
D. Hsu and S. Sabato · 2013
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Lower Bounds on the Oracle Complexity of Convex Optimization Via Information Theory
G. Braun, C. Guzmán, and S. Pokutta · 2014
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Structure learning of antiferromagnetic ising models
G. Bresler, D. Gamarnik, and D. Shah · 2014
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Private empirical risk minimization: Efficient algorithms and tight error bounds
R. Bassily, A. Smith, and A. Thakurta · 2014
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First-order methods of smooth convex optimization with inexact oracle
O. Devolder, F. Glineur, and Y. Nesterov · 2014
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Privacy aware learning
J. Duchi, M.I. Jordan, and M.J. Wainwright · 2014
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The Algorithmic Foundations of Differential Privacy (preprint)
C. Dwork and A. Roth · 2014
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Preventing false discovery in interactive data analysis is hard
M. Hardt and J. Ullman · 2014
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The matching polytope has exponential extension complexity
T. Rothvoß · 2014
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C. Studer, T. Goldstein, W. Yin, and R. Baraniuk · 2014
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Understanding Machine Learning: From Theory to Algorithms
S. Shalev-Shwartz and S. Ben-David · 2014
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Evolvability of real functions
P. Valiant · 2014
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Escaping the local minima via simulated annealing: Optimization of approximately convex functions
A. Belloni, T. Liang, H. Narayanan, and A. Rakhlin · 2015
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Algorithmic stability for adaptive data analysis
R. Bassily, K. Nissim, A. D. Smith, T. Steinke, U. Stemmer, and J. Ullman · 2015
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Preserving statistical validity in adaptive data analysis
C. Dwork, V. Feldman, M. Hardt, T. Pitassi, O. Reingold, and A. Roth · 2015
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Generalization in adaptive data analysis and holdout reuse
C. Dwork, V. Feldman, M. Hardt, T. Pitassi, O. Reingold, and A. Roth · 2015
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On the complexity of random satisfiability problems with planted solutions
V. Feldman, W. Perkins, and S. Vempala · 2015
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On lower complexity bounds for large-scale smooth convex optimization
C. Guzmán and A. Nemirovski · 2015
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Lower bounds on the size of semidefinite programming relaxations
J.R. Lee, P. Raghavendra, and D. Steurer · 2015
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Sum-of-squares lower bounds for planted clique
R. Meka, A. Potechin, and A. Wigderson · 2015
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Interactive fingerprinting codes and the hardness of preventing false discovery
T. Steinke and J. Ullman · 2015
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Private multiplicative weights beyond linear queries
J. Ullman · 2015
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Sharp computational-statistical phase transitions via oracle computational model
Z. Wang, Q. Gu, and H. Liu · 2015
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Dealing with range anxiety in mean estimation via statistical queries
Vitaly Feldman · 2016
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Memory, communication, and statistical queries
J. Steinhardt, G. Valiant, and S. Wager · 2016
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