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Convex-concave min-max problems are ubiquitous in machine learning, and people usually utilize first-order methods (e.g., gradient descent ascent) to find the optimal solution.
The extragradient method for finding saddle points and other problems
GM Korpelevich · 1976
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Arkadi Nemirovski and David Yudin · 1983
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Lipschitz behavior of solutions to convex minimization problems
Jean-Pierre Aubin · 1984
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G. J. Gordon · 1999
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M. Zinkevich · 2003
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Prox-method with rate of convergence O(1/t) for variational inequalities with lipschitz continuous monotone operators and smooth convex-concave saddle point problems
Arkadi Nemirovski · 2004
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Yurii Nesterov and Laura Scrimali · 2006
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Yurii Nesterov · 2007
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Competing in the dark: An efficient algorithm for bandit linear optimization
J. D. Abernethy, E. Hazan, and A. Rakhlin · 2008
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Robust optimization
Aharon Ben-Tal, Laurent El Ghaoui, and Arkadi Nemirovski · 2009
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Arkadi Nemirovski, Anatoli Juditsky, Guanghui Lan, and Alexander Shapiro · 2009
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Primal-dual subgradient methods for convex problems
Y. Nesterov · 2009
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On the complexity of the hybrid proximal extragradient method for the iterates and the ergodic mean
Renato DC Monteiro and Benar Fux Svaiter · 2010
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A first-order primal-dual algorithm for convex problems with applications to imaging
Antonin Chambolle and Thomas Pock · 2011
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Solving variational inequalities with stochastic mirror-prox algorithm
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No-regret algorithms for unconstrained online convex optimization
M. Streeter and B. McMahan · 2012
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Global error bounds for piecewise convex polynomials
Guoyin Li · 2013
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Optimal primal-dual methods for a class of saddle point problems
Yunmei Chen, Guanghui Lan, and Yuyuan Ouyang · 2014
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Generative adversarial nets
Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio · 2014
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Unconstrained online linear learning in Hilbert spaces: Minimax algorithms and normal approximations
H. B. McMahan and F. Orabona · 2014
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Simultaneous model selection and optimization through parameter-free stochastic learning
F. Orabona · 2014
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Online convex optimization with unconstrained domains and losses
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Francis Bach and Kfir Y Levy · 2019
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Matrix-free preconditioning in online learning
A. Cutkosky and T. Sarlos · 2019
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Negative momentum for improved game dynamics
Gauthier Gidel, Reyhane Askari Hemmat, Mohammad Pezeshki, Rémi Le Priol, Gabriel Huang, Simon Lacoste-Julien, and Ioannis Mitliagkas · 2019
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Adaptive scale-invariant online algorithms for learning linear models
M. Kempka, W. Kotłowski, and M. K. Warmuth · 2019
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Interaction matters: A note on non-asymptotic local convergence of generative adversarial networks
Tengyuan Liang and James Stokes · 2019
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A. Cutkosky and K. A. Boahen · 2016
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An accelerated HPE-type algorithm for a class of composite convex-concave saddle-point problems
Yunlong He and Renato DC Monteiro · 2016
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Coin betting and parameter-free online learning
F. Orabona and D. Pál · 2016
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Stochastic online AUC maximization
Yiming Ying, Longyin Wen, and Siwei Lyu · 2016
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Accelerated schemes for a class of variational inequalities
Yunmei Chen, Guanghui Lan, and Yuyuan Ouyang · 2017
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Online learning without prior information
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Towards deep learning models resistant to adversarial attacks
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On lower iteration complexity bounds for the saddle point problems
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Accelerating smooth games by manipulating spectral shapes
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Finite regret and cycles with fixed step-size via alternating gradient descent-ascent
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Halpern iteration for near-optimal and parameter-free monotone inclusion and strong solutions to variational inequalities
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Last iterate is slower than averaged iterate in smooth convex-concave saddle point problems
Noah Golowich, Sarath Pattathil, Constantinos Daskalakis, and Asuman Ozdaglar · 2020
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Explore aggressively, update conservatively: Stochastic extragradient methods with variable stepsize scaling
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Linear lower bounds and conditioning of differentiable games
Adam Ibrahim, Waıss Azizian, Gauthier Gidel, and Ioannis Mitliagkas · 2020
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Scale-invariant unconstrained online learning
W. Kotłowski · 2020
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Near-optimal algorithms for minimax optimization
Tianyi Lin, Chi Jin, and Michael I Jordan · 2020
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A unified analysis of extra-gradient and optimistic gradient methods for saddle point problems: Proximal point approach
Aryan Mokhtari, Asuman Ozdaglar, and Sarath Pattathil · 2020
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Optimal epoch stochastic gradient descent ascent methods for min-max optimization
Yan Yan, Yi Xu, Qihang Lin, Wei Liu, and Tianbao Yang · 2020
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Lower complexity bounds of first-order methods for convex-concave bilinear saddle-point problems
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