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Several widely-used first-order saddle-point optimization methods yield an identical continuous-time ordinary differential equation (ODE) that is identical to that of the Gradient Descent Ascent (GDA) method when derived naively.
K. Arrow, L. Hurwicz: Gradient methods for constrained maxima
1957
Earlier work this paper cites.
B. T. Polyak: Some methods of speeding up the convergence of iteration methods
1964
Earlier work this paper cites.
J. L. Lions, G. Stampacchia: Variational inequalities
1967
Earlier work this paper cites.
H. Lewy, G. Stampacchia: On the regularity of the solution of a variational inequality
1969
Earlier work this paper cites.
G. M. Korpelevich: The extragradient method for finding saddle points and other problems
1976
Earlier work this paper cites.
L. D. Popov: A modification of the Arrow-Hurwicz method for search of saddle points
1980
Earlier work this paper cites.
Y. Nesterov: A method for solving the convex programming problem with convergence rate O ( 1 / k 2 ) O(1/k^{2})
1983
Earlier work this paper cites.
X. Xie: Stable polynomials with complex coefficients
1985
Earlier work this paper cites.
L. Saydy, A. Tits, E. Abed: Guardian maps and the generalized stability of parametrized families of matrices and polynomials
1990
Earlier work this paper cites.
M. Benaïm, M. W. Hirsch: Dynamics of Morse-Smale urn processes
1995
Earlier work this paper cites.
P. Tseng: On linear convergence of iterative methods for the variational inequality problem
1995
Earlier work this paper cites.
U. Helmke, J. B. Moore: Optimization and Dynamical Systems
1996
Earlier work this paper cites.
D. P. Bertsekas: Nonlinear Programming
1999
Earlier work this paper cites.
J. Schropp, I. Singer: A dynamical systems approach to constrained minimization
2000
Earlier work this paper cites.
F. Facchinei, J.-S. Pang: Finite-Dimensional Variational Inequalities and Complementarity Problems
2003
Earlier work this paper cites.
A. Nemirovski: 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
2004
Earlier work this paper cites.
P. Tseng: On accelerated proximal gradient methods for convex-concave optimization
2008
Earlier work this paper cites.
R. D. C. Monteiro, B. F. Svaiter: On the complexity of the hybrid proximal extragradient method for the iterates and the ergodic mean
2010
Earlier work this paper cites.
H. Attouch, P.-E. Maingé, P. Redont: A second-order differential system with Hessian-driven damping; application to non-elastic shock laws
2012
Earlier work this paper cites.
Y. Nesterov: Introductory Lectures on Convex Optimization: A Basic Course
2013
Cited alongside, same era.
J. Pedlosky: Geophysical Fluid Dynamics
2013
Cited alongside, same era.
I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, Y. Bengio: Generative adversarial nets
2014
Cited alongside, same era.
Y. Arjevani, O. Shamir: On the iteration complexity of oblivious first-order optimization algorithms
2016
Cited alongside, same era.
I. Goodfellow: Generative adversarial networks
2016
Cited alongside, same era.
W. Su, S. Boyd, E. J. Candès: A differential equation for modeling Nesterov’s accelerated gradient method: Theory and insights
2016
Cited alongside, same era.
2019
Later among the works it cites.
M. Zhang, J. Lucas, J. Ba, G. E. Hinton: Lookahead optimizer: k steps forward, 1 step back
2019
Later among the works it cites.
W. Azizian, I. Mitliagkas, S. Lacoste-Julien, G. Gidel: A tight and unified analysis of gradient-based methods for a whole spectrum of differentiable games
2020
Later among the works it cites.
H. Berard, G. Gidel, A. Almahairi, P. Vincent, S. Lacoste-Julien: A closer look at the optimization landscapes of generative adversarial networks
2020
Later among the works it cites.
T. Chavdarova, M. Pagliardini, S. U. Stich, F. Fleuret, M. Jaggi: Taming GANs with Lookahead-Minmax
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A. Wibisono, A. Wilson, M. I. Jordan: A variational perspective on accelerated methods in optimization
2016
Cited alongside, same era.
S. Omidshafiei, J. Pazis, C. Amato, J. P. How, J. Vian: Deep decentralized multi-task multi-agent reinforcement learning under partial observability
2017
Cited alongside, same era.
C. Daskalakis, A. Ilyas, V. Syrgkanis, H. Zeng: Training GANs with optimism
2018
Cited alongside, same era.
C. Daskalakis, I. Panageas: The limit points of (optimistic) gradient descent in min-max optimization
2018
Cited alongside, same era.
2018
Cited alongside, same era.
P. Mertikopoulos, C. H. Papadimitriou, G. Piliouras: Cycles in adversarial regularized learning
2018
Cited alongside, same era.
2020
Later among the works it cites.
N. Golowich, S. Pattathil, C. Daskalakis: Tight last-iterate convergence rates for no-regret learning in multi-player games
2020
Later among the works it cites.
N. Golowich, S. Pattathil, C. Daskalakis, A. Ozdaglar: Last iterate is slower than averaged iterate in smooth convex-concave saddle point problems
2020
Later among the works it cites.
2020
Later among the works it cites.
Y.-G. Hsieh, F. Iutzeler, J. Malick, P. Mertikopoulos: Explore aggressively, update conservatively: Stochastic extragradient methods with variable stepsize scaling
2020
Later among the works it cites.
N. Loizou, H. Berard, A. Jolicoeur-Martineau, P. Vincent, S. Lacoste-Julien, I. Mitliagkas: Stochastic Hamiltonian gradient methods for smooth games
2020
Later among the works it cites.
2020
Later among the works it cites.
E. Mazumdar, L. J. Ratliff, S. S. Sastry: On gradient-based learning in continuous games
2020
Later among the works it cites.
A. Mokhtari, A. Ozdaglar, S. Pattathil: Convergence rate of 𝒪 ( 1 / k ) \mathcal{O}(1/k) for optimistic gradient and extra-gradient methods in smooth convex-concave saddle point problems
2020
Later among the works it cites.
Y. Wang, G. Zhang, J. Ba: On solving minimax optimization locally: A follow-the-ridge approach
2020
Later among the works it cites.
J. Abernethy, K. A. Lai, A. Wibisono: Last-iterate convergence rates for min-max optimization: Convergence of Hamiltonian gradient descent and consensus optimization
2021
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T. Fiez, L. J. Ratliff: Local convergence analysis of gradient descent ascent with finite timescale separation
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G. França, M. I. Jordan, R. Vidal: On dissipative symplectic integration with applications to gradient-based optimization
2021
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Y.-P. Hsieh, P. Mertikopoulos, V. Cevher: The limits of min-max optimization algorithms: convergence to spurious non-critical sets
2021
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2021
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