Fetching the paper…
Reading the bibliography…
Despite remarkable empirical success, the training dynamics of generative adversarial networks (GAN), which involves solving a minimax game using stochastic gradients, is still poorly understood.
On the differentiability and the representation of one-parameter semi-group of linear operators
K. Yosida · 1948
Earlier work this paper cites.
Inadmissibility of the usual estimator for the mean of a multivariate normal distribution
C. Stein · 1956
Earlier work this paper cites.
Some Problems in the Theory of Motion Stability
N. N. Krasovskii · 1959
Earlier work this paper cites.
Some extensions of Liapunov’s second method
J. LaSalle · 1960
Earlier work this paper cites.
Estimation with quadratic loss
W. James and C. Stein · 1961
Earlier work this paper cites.
Monotone (nonlinear) operators in Hilbert space
G. J. Minty · 1962
Earlier work this paper cites.
Proximité et dualité dans un espace hilbertien
J. J. Moreau · 1965
Earlier work this paper cites.
Fixed points of nonexpanding maps
B. Halpern · 1967
Earlier work this paper cites.
Monotone operators associated with saddle-functions and minimax problems
R. T. Rockafellar · 1970
Earlier work this paper cites.
A convergence theorem for non negative almost supermartingales and some applications
H. Robbins and D. Siegmund · 1971
Earlier work this paper cites.
The extragradient method for finding saddle points and other problems
G. M. Korpelevich · 1976
Earlier work this paper cites.
On the weak convergence of an ergodic iteration for the solution of variational inequalities for monotone operators in Hilbert space
R. E. Bruck · 1977
Earlier work this paper cites.
On Cezari’s convergence of the steepest descent method for approximating saddle point of convex-concave functions
A. Nemirovski and D. Yudin · 1978
Earlier work this paper cites.
A modification of the Arrow–Hurwicz method for search of saddle points
L. D. Popov · 1980
Earlier work this paper cites.
Differential Inclusions: Set-Valued Maps and Viability Theory
J. P. Aubin and A. Cellina · 1984
Earlier work this paper cites.
Introduction to optimization
B. T. Polyak · 1987
Earlier work this paper cites.
Approximation of fixed points of nonexpansive mappings
R. Wittmann · 1992
Earlier work this paper cites.
A modified forward-backward splitting method for maximal monotone mappings
P. Tseng · 2000
Earlier work this paper cites.
The dynamics of elastic shocks via epigraphical regularization of a differential inclusion
H. Attouch, A. Cabot, and P. Redont · 2002
Earlier work this paper cites.
Robust stochastic approximation approach to stochastic programming
A. Nemirovski, A. Juditsky, G. Lan, and A. Shapiro · 2009
Earlier work this paper cites.
Solving variational inequalities with stochastic mirror-prox algorithm
A. Juditsky, A. Nemirovski, and C. Tauvel · 2011
Earlier work this paper cites.
Non-asymptotic analysis of stochastic approximation algorithms for machine learning
E. Moulines and F. Bach · 2011
Earlier work this paper cites.
Online optimization with gradual variations
C.-K. Chiang, T. Yang, C.-J. Lee, M. Mahdavi, C.-J. Lu, R. Jin, and S. Zhu · 2012
Earlier work this paper cites.
Online learning with predictable sequences
A. Rakhlin and K. Sridharan · 2013
Earlier work this paper cites.
Optimization, learning, and games with predictable sequences
A. Rakhlin and K. Sridharan · 2013
Cited alongside, same era.
Generative adversarial nets
I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio · 2014
Cited alongside, same era.
An extragradient algorithm for monotone variational inequalities
Y. V. Malitsky and V. V. Semenov · 2014
Cited alongside, same era.
A differential equation for modeling Nesterov’s accelerated gradient method: Theory and insights
W. Su, S. Boyd, and E. Candes · 2014
Cited alongside, same era.
Projected reflected gradient methods for monotone variational inequalities
Y. Malitsky · 2015
Cited alongside, same era.
Fast convergence of regularized learning in games
V. Syrgkanis, A. Agarwal, H. Luo, and R. E. Schapire · 2015
Cited alongside, same era.
Global convergence to the equilibrium of GANs using variational inequalities
I. Gemp and S. Mahadevan · 2018
Later among the works it cites.
A forward-backward splitting method for monotone inclusions without cocoercivity
Y. Malitsky and M. K. Tam · 2018
Later among the works it cites.
Which training methods for GANs do actually converge?
L. Mescheder, A. Geiger, and S. Nowozin · 2018
Later among the works it cites.
Spectral normalization for generative adversarial networks
T. Miyato, T. Kataoka, M. Koyama, and Y. Yoshida · 2018
Later among the works it cites.
Improving the improved training of Wasserstein GANs: A consistency term and its dual effect
X. Wei, B. Gong, Z. Liu, W. Lu., and L. Wang · 2018
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Nips 2016 tutorial: Generative adversarial networks
I. Goodfellow · 2016
Cited alongside, same era.
Unsupervised representation learning with deep convolutional generative adversarial networks
A. Radford, L. Metz, and S. Chintala · 2016
Cited alongside, same era.
Primer on monotone operator methods
E. K. Ryu and S. P. Boyd · 2016
Cited alongside, same era.
Towards principled methods for training generative adversarial networks
M. Arjovsky and L. Bottou · 2017
Cited alongside, same era.
Wasserstein generative adversarial networks
M. Arjovsky, S. Chintala, and L. Bottou · 2017
Cited alongside, same era.
Convex Analysis and Monotone Operator Theory in Hilbert Spaces
H. H. Bauschke and P. L. Combettes · 2017
Cited alongside, same era.
Stabilizing adversarial nets with prediction methods
A. Yadav, S. Shah, Z. Xu, D. Jacobs, and T. Goldstein · 2018
Later among the works it cites.
Convergence of inertial dynamics and proximal algorithms governed by maximally monotone operators
H. Attouch and J. Peypouquet · 2019
Closest in time.
Reducing noise in GAN training with variance reduced extragradient
T. Chavdarova, G. Gidel, F. Fleuret, and S. Lacoste-Julien · 2019
Closest in time.
Shadow Douglas–Rachford splitting for monotone inclusions
E. R. Csetnek, Y. Malitsky, and M. K. Tam · 2019
Closest in time.
Last-iterate convergence: Zero-sum games and constrained min-max optimization
C. Daskalakis and I. Panageas · 2019
Closest in time.
Stochastic subgradient method converges on tame functions
Damek Davis, Dmitriy Drusvyatskiy, Sham Kakade, and Jason D. Lee · 2019
Closest in time.
Lecture notes on probability theory: Stanford statistics 310
A. Dembo · 2019
Closest in time.
A variational inequality perspective on generative adversarial networks
G. Gidel, H. Berard, G. Vignoud, P. Vincent, and S. Lacoste-Julien · 2019
Closest in time.
Negative momentum for improved game dynamics
G. Gidel, M. Pezeshki R. A. Hemmat, R. Lepriol, G. Huang, S. Lacoste-Julien, and I. Mitliagkas · 2019
Closest in time.
Interaction matters: A note on non-asymptotic local convergence of generative adversarial networks
T. Liang and J. Stokes · 2019
Closest in time.
Golden ratio algorithms for variational inequalities
Y. Malitsky · 2019
Closest in time.
Optimistic mirror descent in saddle-point problems: Going the extra(-gradient) mile
P. Mertikopoulos, B. Lecouat, H. Zenati, C.-S. Foo, V. Chandrasekhar, and G. Piliouras · 2019
Closest in time.
A. Mokhtari, A. Ozdaglar, and S. Pattathil · 2019
Closest in time.
Open questions about generative adversarial networks (online article)
A. Odena · 2019
Closest in time.
Training GANs with centripetal acceleration
W. Peng, Y. Dai, H. Zhang, and L. Cheng · 2019
Closest in time.
Stochastic first-order methods: non-asymptotic and computer-aided analyses via potential functions
A. Taylor and F. Bach · 2019
Closest in time.
The unusual effectiveness of averaging in GAN training
Y. Yazıcı, C.-S. Foo, S. Winkler, K.-H. Yap, G. Piliouras, and V. Chandrasekhar · 2019
Closest in time.
Backward-forward-reflected-backward splitting for three operator monotone inclusions
J. Rieger and M. K. Tam · 2020
Closest in time.