Competitive Gradient Optimization

Description

These are some examples of non-convex non-concave functions for which the CGO algorithm finds the saddle points for some choice of parameter alpha.

$x^2y$ : Shrinking region with increasing $\alpha$

$x^2y+xy$ : Convergence to Nash with large $\alpha$

$f(x, y) = (x − 1/2)(y − 1/2) +\frac{1}{3}e^{−(x − 1/4)^2 − (y − 3/4)^2}$ : Vanishing incoherent region

Name		Name	Last commit message	Last commit date
CGD_vs_CGO_GaussianMixture_GAN.ipynb		CGD_vs_CGO_GaussianMixture_GAN.ipynb
CGO.ipynb		CGO.ipynb
CGO_Pytorch_GMM		CGO_Pytorch_GMM
Not MVI.gif		Not MVI.gif
README.md		README.md
Shrinking region with alpha.ipynb		Shrinking region with alpha.ipynb
Shrinkning Region.gif		Shrinkning Region.gif
Weak-MVI CGO.ipynb		Weak-MVI CGO.ipynb
alpha-MVI but not weak-MVI.ipynb		alpha-MVI but not weak-MVI.ipynb
vanishing in exponential.gif		vanishing in exponential.gif