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Owing to their stability and convergence speed, extragradient methods have become a staple for solving large-scale saddle-point problems in machine learning.
On a stochastic approximation method
Chung, K.-L · 1954
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A convergence theorem for non negative almost supermartingales and some applications
Robbins, H. and Siegmund, D · 1971
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The extragradient method for finding saddle points and other problems
Korpelevich, G. M · 1976
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A modification of the Arrow–Hurwicz method for search of saddle points
Popov, L. D · 1980
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Problem Complexity and Method Efficiency in Optimization
Nemirovski, A. S. and Yudin, D. B · 1983
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Introduction to Optimization
Polyak, B. T · 1987
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Error bounds and convergence analysis of feasible descent methods: a general approach
Luo, Z.-Q. and Tseng, P · 1993
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On linear convergence of iterative methods for the variational inequality problem
Tseng, P · 1995
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Evolutionary Games and Population Dynamics
Hofbauer, J. and Sigmund, K · 1998
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Finite-Dimensional Variational Inequalities and Complementarity Problems
Facchinei, F. and Pang, J.-S · 2003
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Convergence rate analysis of iteractive algorithms for solving variational inequality problems
Solodov, M. V · 2003
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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
Nemirovski, A. S · 2004
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Dual extrapolation and its applications to solving variational inequalities and related problems
Nesterov, Y · 2007
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Population Games and Evolutionary Dynamics
Sandholm, W. H · 2010
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Solving variational inequalities with stochastic mirror-prox algorithm
Juditsky, A., Nemirovski, A. S., and Tauvel, C · 2011
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Regularized iterative stochastic approximation methods for stochastic variational inequality problems
Koshal, J., Nedic, A., and Shanbhag, U. V · 2012
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Optimization despite chaos: Convex relaxations to complex limit sets via Poincaré recurrence
Piliouras, G. and Shamma, J. S · 2014
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Extragradient method with variance reduction for stochastic variational inequalities
Iusem, A. N., Jofré, A., Oliveira, R. I., and Thompson, P · 2017
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Gradient descent gan optimization is locally stable
Nagarajan, V. and Kolter, J. Z · 2017
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Multiplicative weights update with constant step-size in congestion games: Convergence, limit cycles and chaos
Palaiopanos, G., Panageas, I., and Piliouras, G · 2017
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Training GANs with optimism
Extra-gradient with player sampling for provable fast convergence in n-player games
Jelassi, S., Enrich, C. D., Scieur, D., Mensch, A., and Bruna, J · 2019
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Optimal stochastic extragradient schemes for pseudomonotone stochastic variational inequality problems and their variants
Kannan, A. and Shanbhag, U. V · 2019
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Interaction matters: A note on non-asymptotic local convergence of generative adversarial networks
Liang, T. and Stokes, J · 2019
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Golden ratio algorithms for variational inequalities
Malitsky, Y · 2019
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Optimistic mirror descent in saddle-point problems: Going the extra (gradient) mile
Mertikopoulos, P., Lecouat, B., Zenati, H., Foo, C.-S., Chandrasekhar, V., and Piliouras, G · 2019
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Daskalakis, C., Ilyas, A., Syrgkanis, V., and Zeng, H · 2018
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Cycles in adversarial regularized learning
Mertikopoulos, P., Papadimitriou, C. H., and Piliouras, G · 2018
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Which training methods for gans do actually converge?
Mescheder, L., Nowozin, S., and Geiger, A · 2018
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Reducing noise in gan training with variance reduced extragradient
Chavdarova, T., Gidel, G., Fleuret, F., and Lacoste-Julien, S · 2019
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Vortices instead of equilibria in minmax optimization: Chaos and butterfly effects of online learning in zero-sum games
Cheung, Y. K. and Piliouras, G · 2019
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An optimal multistage stochastic gradient method for minimax problems
Fallah, A., Ozdaglar, A., and Pattathil, S · 2019
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Poincaré recurrence, cycles and spurious equilibria in gradient-descent-ascent for non-convex non-concave zero-sum games
Flokas, L., Vlatakis-Gkaragkounis, E. V., and Piliouras, G · 2019
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Peng, W., Dai, Y.-H., Zhang, H., and Cheng, L · 2019
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Ryu, E. K., Yuan, K., and Yin, W · 2019
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Painless stochastic gradient: Interpolation, line-search, and convergence rates
Vaswani, S., Mishkin, A., Laradji, I., Schmidt, M., Gidel, G., and Lacoste-Julien, S · 2019
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Accelerating smooth games by manipulating spectral shapes
Azizian, W., Scieur, D., Mitliagkas, I., Lacoste-Julien, S., and Gidel, G · 2020
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Towards better understanding of adaptive gradient algorithms in generative adversarial nets
Liu, M., Mroueh, Y., Ross, J., Zhang, W., Cui, X., Das, P., and Yang, T · 2020
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Stochastic hamiltonian gradient methods for smooth games
Loizou, N., Berard, H., Jolicoeur-Martineau, A., Vincent, P., Lacoste-Julien, S., and Mitliagkas, I · 2020
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Revisiting stochastic extragradient
Mishchenko, K., Kovalev, D., Shulgin, E., Richtárik, P., and Malitsky, Y · 2020
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A unified analysis of extra-gradient and optimistic gradient methods for saddle point problems: proximal point approach
Mokhtari, A., Ozdaglar, A., and Pattathil, S · 2020
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Convergence behaviour of some gradient-based methods on bilinear zero-sum games
Zhang, G. and Yu, Y · 2020
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