A metric-space theory of gradient descent-ascent flows is developed via evolution variational inequalities, yielding existence, uniqueness, and exponential convergence for Wasserstein GDA under strong convexity-concavity.
A Gradient Method for Approximating Saddle Points and Constrained Maxima
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On gradient descent-ascent flows in metric spaces
A metric-space theory of gradient descent-ascent flows is developed via evolution variational inequalities, yielding existence, uniqueness, and exponential convergence for Wasserstein GDA under strong convexity-concavity.