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Minimax optimization has found extensive applications in modern machine learning, in settings such as generative adversarial networks (GANs), adversarial training and multi-agent reinforcement learning.
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Irving L Glicksberg · 1952
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Theory of games and economic behavior
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Mishael Zedek · 1965
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Yurii Gavrilovich Evtushenko · 1974
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On the weak convergence of an ergodic iteration for the solution of variational inequalities for monotone operators in hilbert space
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Arkadi Nemirovski · 1981
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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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Game theory
Roger B Myerson · 2013
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Constrained optimization and Lagrange multiplier methods
Dimitri P Bertsekas · 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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Convex optimization: Algorithms and complexity
Sébastien Bubeck · 2015
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Convex analysis
Ralph Tyrell Rockafellar · 2015
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The non-convex burer-monteiro approach works on smooth semidefinite programs
Nicolas Boumal, Vlad Voroninski, and Afonso Bandeira · 2016
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Introduction to online convex optimization
Elad Hazan · 2016
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Deep decentralized multi-task multi-agent reinforcement learning under partial observability
Shayegan Omidshafiei, Jason Pazis, Christopher Amato, Jonathan P How, and John Vian · 2017
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Local saddle point optimization: A curvature exploitation approach
Leonard Adolphs, Hadi Daneshmand, Aurelien Lucchi, and Thomas Hofmann · 2018
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The limit points of (optimistic) gradient descent in min-max optimization
Constantinos Daskalakis and Ioannis Panageas · 2018
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Damek Davis and Dmitriy Drusvyatskiy · 2018
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Sanjeev Arora, Rong Ge, Yingyu Liang, Tengyu Ma, and Yi Zhang · 2017
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Saddle-point dynamics: conditions for asymptotic stability of saddle points
Ashish Cherukuri, Bahman Gharesifard, and Jorge Cortes · 2017
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No spurious local minima in nonconvex low rank problems: A unified geometric analysis
Rong Ge, Chi Jin, and Yi Zheng · 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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Towards deep learning models resistant to adversarial attacks
Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu · 2017
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Gradient descent gan optimization is locally stable
Vaishnavh Nagarajan and J Zico Kolter · 2017
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Gauthier Gidel, Reyhane Askari Hemmat, Mohammad Pezeshki, Gabriel Huang, Remi Lepriol, Simon Lacoste-Julien, and Ioannis Mitliagkas · 2018
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Finding mixed nash equilibria of generative adversarial networks
Ya-Ping Hsieh, Chen Liu, and Volkan Cevher · 2018
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Solving weakly-convex-weakly-concave saddle-point problems as weakly-monotone variational inequality
Qihang Lin, Mingrui Liu, Hassan Rafique, and Tianbao Yang · 2018
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On the convergence of gradient-based learning in continuous games
Eric Mazumdar and Lillian J Ratliff · 2018
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Non-convex min-max optimization: Provable algorithms and applications in machine learning
Hassan Rafique, Mingrui Liu, Qihang Lin, and Tianbao Yang · 2018
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Convergence of learning dynamics in stackelberg games
Tanner Fiez, Benjamin Chasnov, and Lillian J Ratliff · 2019
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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
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Solving a class of non-convex min-max games using iterative first order methods
Maher Nouiehed, Maziar Sanjabi, Jason D Lee, and Meisam Razaviyayn · 2019
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