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Motivated by applications in Optimization, Game Theory, and the training of Generative Adversarial Networks, the convergence properties of first order methods in min-max problems have received extensive study.
Zur theorie der gesellschaftsspiele
J Von Neumann · 1928
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Iterative solutions of games by fictitious play
G.W Brown · 1951
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An iterative method of solving a game
J. Robinson · 1951
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An analog of the minimax theorem for vector payoffs
David Blackwell · 1956
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Global Stability of Dynamical Systems
Michael Shub · 1987
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Prediction, Learning, and Games
Nikolo Cesa-Bianchi and Gabor Lugosi · 2006
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Discrete Dynamical Systems
Oded Galor · 2007
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Mohammad Sal Moslehian · 2011
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The equivalence of linear programs and zero-sum games
Ilan Adler · 2013
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Online learning with predictable sequences
Alexander Rakhlin and Karthik Sridharan · 2013
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Generative adversarial nets
Ian J. Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron C. Courville, and Yoshua Bengio · 2014
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Natural selection as an inhibitor of genetic diversity: Multiplicative weights updates algorithm and a conjecture of haploid genetics
Ruta Mehta, Ioannis Panageas, and Georgios Piliouras · 2015
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Local maxima in the likelihood of gaussian mixture models: Structural results and algorithmic consequences
Chi Jin, Yuchen Zhang, Sivaraman Balakrishnan, Martin J. Wainwright, and Michael I. Jordan · 2016
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Gradient descent only converges to minimizers
Saddle-point dynamics: Conditions for asymptotic stability of saddle points
Ashish Cherukuri, Bahman Gharesifard, and Jorge Cortés · 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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Multiplicative weights update with constant step-size in congestion games: Convergence, limit cycles and chaos
Gerasimos Palaiopanos, Ioannis Panageas, and Georgios Piliouras · 2017
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Gradient descent only converges to minimizers: Non-isolated critical points and invariant regions
Ioannis Panageas and Georgios Piliouras · 2017
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Training gans with optimism
Constantinos Daskalakis, Andrew Ilyas, Vasilis Syrgkanis, and Haoyang Zeng · 2018
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Jason D. Lee, Max Simchowitz, Michael I. Jordan, and Benjamin Recht · 2016
Cited alongside, same era.
Wasserstein generative adversarial networks
Martín Arjovsky, Soumith Chintala, and Léon Bottou · 2017
Cited alongside, same era.
Rock-paper-scissors, differential games and biological diversity
Tung Mai, Milena Mihail, Ioannis Panageas, Will Ratcliff, Vijay V. Vazirani, and Peter Yunker · 2018
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Cycles in adversarial regularized learning
Panayotis Mertikopoulos, Christos Papadimitriou, and Georgios Piliouras · 2018
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