Fetching the paper…
Reading the bibliography…
We study the stochastic bilinear minimax optimization problem, presenting an analysis of the same-sample Stochastic ExtraGradient (SEG) method with constant step size, and presenting variations of the method that yield favorable convergence.
On lower iteration complexity bounds for the saddle point problems
Junyu Zhang, Mingyi Hong, and Shuzhong Zhang · 1912
Earlier work this paper cites.
Theory of Games and Economic Behavior
Oskar Morgenstern and John Von Neumann · 1944
Earlier work this paper cites.
An analog of the minimax theorem for vector payoffs
David Blackwell · 1956
Earlier work this paper cites.
The extragradient method for finding saddle points and other problems
G.M. Korpelevich · 1976
Earlier work this paper cites.
On linear convergence of iterative methods for the variational inequality problem
Paul Tseng · 1995
Earlier work this paper cites.
Numerical Linear Algebra
Lloyd N Trefethen and David Bau III · 1997
Earlier work this paper cites.
The mnist database of handwritten digits
Yann LeCun · 1998
Earlier work this paper cites.
Prox-method with rate of convergence O ( 1 / t ) {O}(1/t) for variational inequalities with Lipschitz continuous monotone operators and smooth convex-concave saddle point problems
Arkadi Nemirovski · 2004
Earlier work this paper cites.
Prediction, Learning, and Games
Nicolo Cesa-Bianchi and Gábor Lugosi · 2006
Earlier work this paper cites.
Large deviations of vector-valued martingales in 2-smooth normed spaces
Anatoli Juditsky and Arkadii S Nemirovski · 2008
Earlier work this paper cites.
Robust stochastic approximation approach to stochastic programming
Arkadi Nemirovski, Anatoli Juditsky, Guanghui Lan, and Alexander Shapiro · 2009
Earlier work this paper cites.
Solving variational inequalities with stochastic mirror-prox algorithm
Anatoli Juditsky, Arkadi Nemirovski, and Claire Tauvel · 2011
Earlier work this paper cites.
Generative adversarial networks
Ian J Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio · 2014
Earlier work this paper cites.
Convergence rate of stochastic gradient with constant step size
Mark Schmidt · 2014
Earlier work this paper cites.
Adaptive restart for accelerated gradient schemes
Brendan O’Donoghue and Emmanuel Candes · 2015
Earlier work this paper cites.
Unsupervised representation learning with deep convolutional generative adversarial networks
Alec Radford, Luke Metz, and Soumith Chintala · 2015
Earlier work this paper cites.
Harder, better, faster, stronger convergence rates for least-squares regression
Aymeric Dieuleveut, Nicolas Flammarion, and Francis Bach · 2016
Cited alongside, same era.
NIPS2016 Tutorial: Generative Adversarial Networks
Ian Goodfellow · 2016
Cited alongside, same era.
Wasserstein generative adversarial networks
Martin Arjovsky, Soumith Chintala, and Léon Bottou · 2017
Cited alongside, same era.
Gans trained by a two time-scale update rule converge to a local nash equilibrium
Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter · 2017
Cited alongside, same era.
Extragradient method with variance reduction for stochastic variational inequalities
Alfredo N Iusem, Alejandro Jofré, Roberto Imbuzeiro Oliveira, and Philip Thompson · 2017
Cited alongside, same era.
On finding local Nash equilibria (and only local Nash equilibria) in zero-sum games
Eric V Mazumdar, Michael I Jordan, and S Shankar Sastry · 2019
Later among the works it cites.
A closer look at the optimization landscapes of generative adversarial networks
Hugo Berard, Gauthier Gidel, Amjad Almahairi, Pascal Vincent, and Simon Lacoste-Julien · 2020
Later among the works it cites.
Last iterate is slower than averaged iterate in smooth convex-concave saddle point problems
Noah Golowich, Sarath Pattathil, Constantinos Daskalakis, and Asuman Ozdaglar · 2020
Later among the works it cites.
Explore aggressively, update conservatively: Stochastic extragradient methods with variable stepsize scaling
Yu-Guan Hsieh, Franck Iutzeler, Jérôme Malick, and Panayotis Mertikopoulos · 2020
Later among the works it cites.
Linear lower bounds and conditioning of differentiable games
Adam Ibrahim, Waıss Azizian, Gauthier Gidel, and Ioannis Mitliagkas · 2020
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
The mechanics of n n -player differentiable games
David Balduzzi, Sebastien Racaniere, James Martens, Jakob Foerster, Karl Tuyls, and Thore Graepel · 2018
Cited alongside, same era.
The limit points of (optimistic) gradient descent in min-max optimization
Constantinos Daskalakis and Ioannis Panageas · 2018
Cited alongside, same era.
Training GANs with optimism
Constantinos Daskalakis, Andrew Ilyas, Vasilis Syrgkanis, and Haoyang Zeng · 2018
Cited alongside, same era.
Towards deep learning models resistant to adversarial attacks
Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu · 2018
Cited alongside, same era.
Lectures on Convex Optimization , volume 137
Yurii Nesterov · 2018
Cited alongside, same era.
Local saddle point optimization: A curvature exploitation approach
Leonard Adolphs, Hadi Daneshmand, Aurelien Lucchi, and Thomas Hofmann · 2019
Cited alongside, same era.
The “ η \eta -trick” or the effectiveness of reweighted least-squares, 2019
Francis Bach · 2019
Cited alongside, same era.
On the adaptivity of stochastic gradient-based optimization
Lihua Lei and Michael I Jordan · 2020
Later among the works it cites.
Momentum and stochastic momentum for stochastic gradient, newton, proximal point and subspace descent methods
Nicolas Loizou and Peter Richtárik · 2020
Later among the works it cites.
Stochastic Hamiltonian gradient methods for smooth games
Nicolas Loizou, Hugo Berard, Alexia Jolicoeur-Martineau, Pascal Vincent, Simon Lacoste-Julien, and Ioannis Mitliagkas · 2020
Later among the works it cites.
Revisiting stochastic extragradient
Konstantin Mishchenko, Dmitry Kovalev, Egor Shulgin, Peter Richtárik, and Yura Malitsky · 2020
Later among the works it cites.
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
Later among the works it cites.
Sharpness, restart, and acceleration
Vincent Roulet and Alexandre d’Aspremont · 2020
Later among the works it cites.
On the convergence of the stochastic heavy ball method
Othmane Sebbouh, Robert M Gower, and Aaron Defazio · 2020
Later among the works it cites.
Stochastic variance reduction for variational inequality methods
Ahmet Alacaoglu and Yura Malitsky · 2021
Closest in time.
SGD for structured nonconvex functions: Learning rates, minibatching and interpolation
Robert Gower, Othmane Sebbouh, and Nicolas Loizou · 2021
Closest in time.
A simple nearly optimal restart scheme for speeding up first-order methods
James Renegar and Benjamin Grimmer · 2021
Closest in time.
Linear last-iterate convergence in constrained saddle-point optimization
Chen-Yu Wei, Chung-Wei Lee, Mengxiao Zhang, and Haipeng Luo · 2021
Closest in time.