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Smooth minimax games often proceed by simultaneous or alternating gradient updates.
On lower iteration complexity bounds for the saddle point problems
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Iterative methods for sparse linear systems
Yousef Saad · 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
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On accelerated proximal gradient methods for convex-concave optimization
Paul Tseng · 2008
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Robust optimization , volume 28
Aharon Ben-Tal, Laurent El Ghaoui, and Arkadi Nemirovski · 2009
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Learning multiple layers of features from tiny images
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Algorithmic game theory
Tim Roughgarden · 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 strongly monotone variational and quasi-variational inequalities
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Reading digits in natural images with unsupervised feature learning
Yuval Netzer, Tao Wang, Adam Coates, Alessandro Bissacco, Bo Wu, and Andrew Y Ng · 2011
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Optimization, learning, and games with predictable sequences
Alexander Rakhlin and Karthik Sridharan · 2013
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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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Unsupervised representation learning with deep convolutional generative adversarial networks
Alec Radford, Luke Metz, and Soumith Chintala · 2015
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Gradient descent only converges to minimizers
Jason D Lee, Max Simchowitz, Michael I Jordan, and Benjamin Recht · 2016
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Analysis and design of optimization algorithms via integral quadratic constraints
Laurent Lessard, Benjamin Recht, and Andrew Packard · 2016
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Improved techniques for training gans
Tim Salimans, Ian J Goodfellow, Wojciech Zaremba, Vicki Cheung, Alec Radford, and Xi Chen · 2016
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Wasserstein generative adversarial networks
On the convergence of single-call stochastic extra-gradient methods
Yu-Guan Hsieh, Franck Iutzeler, Jérôme Malick, and Panayotis Mertikopoulos · 2019
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Differentiable game mechanics
Alistair Letcher, David Balduzzi, Sébastien Racaniere, James Martens, Jakob N Foerster, Karl Tuyls, and Thore Graepel · 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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Optimistic mirror descent in saddle-point problems: Going the extra(-gradient) mile
Panayotis Mertikopoulos, Bruno Lecouat, Houssam Zenati, Chuan-Sheng Foo, Vijay Chandrasekhar, and Georgios Piliouras · 2019
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Competitive gradient descent
Florian Schaefer and Anima Anandkumar · 2019
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On solving minimax optimization locally: A follow-the-ridge approach
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Martin Arjovsky, Soumith Chintala, and Léon Bottou · 2017
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Stochastic variance reduction methods for policy evaluation
Simon S Du, Jianshu Chen, Lihong Li, Lin Xiao, and Dengyong Zhou · 2017
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Improved training of wasserstein gans
Ishaan Gulrajani, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron C Courville · 2017
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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
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First-order methods almost always avoid saddle points
Jason D Lee, Ioannis Panageas, Georgios Piliouras, Max Simchowitz, Michael I Jordan, and Benjamin Recht · 2017
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The numerics of gans
Lars Mescheder, Sebastian Nowozin, and Andreas Geiger · 2017
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Multiplicative weights update in zero-sum games
James P Bailey and Georgios Piliouras · 2018
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Yuanhao Wang, Guodong Zhang, and Jimmy Ba · 2019
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Finite regret and cycles with fixed step-size via alternating gradient descent-ascent
James P Bailey, Gauthier Gidel, and Georgios Piliouras · 2020
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Alternating proximal-gradient steps for (stochastic) nonconvex-concave minimax problems
Radu Ioan Boţ and Axel Böhm · 2020
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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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Near-optimal algorithms for minimax optimization
Tianyi Lin, Chi Jin, and Michael I. Jordan · 2020
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Improved algorithms for convex-concave minimax optimization
Yuanhao Wang and Jian Li · 2020
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Zi Xu, Huiling Zhang, Yang Xu, and Guanghui Lan · 2020
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Convergence of gradient methods on bilinear zero-sum games
Guojun Zhang and Yaoliang Yu · 2020
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Taming GANs with lookahead-minmax
Tatjana Chavdarova, Matteo Pagliardini, Sebastian U Stich, François Fleuret, and Martin Jaggi · 2021
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Local convergence analysis of gradient descent ascent with finite timescale separation
Tanner Fiez and Lillian J Ratliff · 2021
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Dippa: An improved method for bilinear saddle point problems
Guangzeng Xie, Yuze Han, and Zhihua Zhang · 2021
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On the suboptimality of negative momentum for minimax optimization
Guodong Zhang and Yuanhao Wang · 2021
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A unified analysis of first-order methods for smooth games via integral quadratic constraints
Guodong Zhang, Xuchan Bao, Laurent Lessard, and Roger Grosse · 2021
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