Mirror descent in saddle-point problems: Going the extra (gradient) mile

By Panayotis Mertikopoulos, Houssam Zenati, Bruno Lecouat, Chuan-Sheng Foo, Vijay Ramaseshan Chandrasekhar, Georgios Piliouras. 2018

33 citations recorded by the source corpus.

Subfields: Optimization & Training

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Citations in the corpus

A Tight and Unified Analysis of Extragradient for a Whole Spectrum of Differentiable Games (2019, background): “More recently, Mertikopoulos et al. (2019) proved that, for a broad class of saddle-point problems, its stochastic version converges almost surely to a solution.”
A Variational Inequality Perspective on Generative Adversarial Networks (2018, neutral): “(4)Independent works [Mertikopoulos et al., 2018] and [Yazıcı et al.”
Last Iterate is Slower than Averaged Iterate in Smooth Convex-Concave Saddle Point Problems (2020, background): “The proof of Theorem 10 proceeds by ﬁrst using the well-known fact (Facchinei and Pang (2003); Mertikopoulos et al. (2018); Mokhtari et al. (2019a)) that for any T ∈ N , there is some t ∗ ∈ { 1 , 2 , . . . , T } so that the t ∗ th iterate z ( t ∗ ) = ( x ( t ∗ ) , y ( t ∗ ) ) obtains the upper…”
Variance Reduction for Matrix Games (2019, background): “In recent years, minimax formulations for neural network training rose to prominence [14, 20], leading to intense interest in algorithms for solving large scale minimax games [10, 13, 18, 9, 16, 21].”
On Finding Local Nash Equilibria (and Only Local Nash Equilibria) in Zero-Sum Games (2019, unknown): “A second promising line of research into theoretically sound methods of ﬁnding the Nash equilibria of zero-sum games has approached the issue from the perspective of variational inequalities (Mertikopoulos et al., 2018a; Gidel et al., 2018).”
Differentiable Game Mechanics (2019, background): “A variety of game-theoretically or minimax motivated modiﬁcations to vanilla gradient descent have been investigated in the context of GANs, see Mertikopoulos et al. (2019); Gidel et al. (2018).”
Solving a Class of Non-Convex Min-Max Games Using Iterative First Order Methods (2019, methodology): “This setting has been extensively studied and different algorithms have been developed for finding a Nash equilibrium [46, 21, 44, 29, 40, 23, 26, 43, 18, 45].”