Characterization and computation of local Nash equilibria in continuous games

By Lillian J. Ratliff, Samuel A. Burden, S. Sastry, Min Μ. 2013

235 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Management Science and Operations Research, Numerical Analysis, Optimization & Training, Game & Decision Theory

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

In Management Science and Operations Research

In Numerical Analysis

In Optimization & Training

In Game & Decision Theory

Citations in the corpus

The Numerics of GANs (2017, methodology): “It can be shown that simultaneous gradient ascent converges locally to a Nash-equilibrium for a zero-sum game, if the Hessian of both players is negative definite [16, 22] and the learning rate is small enough.”
NIPS 2016 Tutorial: Generative Adversarial Networks (2016, methodology): “Here, we use the terminology of local differential Nash equilibria (Ratliff et al., 2013).”
How to Train Your DRAGAN (2017, background): “We hypothesize that the difficulty in training GANs, especially due to mode collapse, results from the existence of spurious local Nash Equilibria in non-convex games [8].”
Diffusion Models: A Comprehensive Survey of Methods and Applications (2022, background): “Namely, the goal of GAN optimization is to achieve Nash equilibrium [193].”
A Survey on Generative Adversarial Networks: Variants, Applications, and Training (2020, methodology): “ causes massive fluctuation and instability becomes poor, as shown in Figure 10. Figure 10: With more iteration, the oscillation grows-up, which causes more and more, training instability. Image from [191]. 4.1.2 Internal covariate shift Internal Covariate Shift (ICS) occurs when the input distribut”
On Finding Local Nash Equilibria (and Only Local Nash Equilibria) in Zero-Sum Games (2019, unknown): “As was shown in Ratliff et al. (2013), generically, local Nash equilibria will satisfy slightly stronger conditions, namely they will be differential Nash equilibria (DNE): Here D x f and D y f denote the partial derivatives of f with respect to x and y respectively, and D 2 xx f and D 2 yy f…”
Generative adversarial networks: introduction and outlook (2017, methodology): “The optimization process of GANs is a minimax game process, and the optimization goal is to reach Nash equilibrium [4], where the generator is considered to have captured the distribution of real samples.”
On the convergence of single-call stochastic extra-gradient methods (2019, background): “As for saddle-point problems and smooth games, variants of this condition can be found in several different sources, see e.g., [16, 24, 29, 40, 41] and references therein.”
A Review on Generative Adversarial Networks: Algorithms, Theory, and Applications (2020, background): “That is, the optimization goal is to reach Nash equilibrium [1].”
On Finding Local Nash Equilibria (and Only Local Nash Equilibria) in Zero-Sum Games (2019, background): “ch equilibria are locally optimal for both players with respect to their own decision variable, meaning that neither player has an incentive to unilaterally deviate from such a point. As was shown in Ratliff et al. (2013), generically, local Nash equilibria will satisfy slightly stronger conditions,”
Deep learning in medical image registration: a survey (2019, background): “The goal for training GANs is to converge to a diﬀerentiable Nash Equilibrium [99], at which point generated data and real data are indistinguishable [37].”
On the Characterization of Local Nash Equilibria in Continuous Games (2014, result): “The results in this paper extend our earlier work [23], [24] by generalizing the second-order non-degeneracy condition [23, Thm.”