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Riemannian ascent--descent for nonconvex nonconcave minimax landscapes: convergence to basin saddle points and applications to distributionally robust optimization
Rishabh Dixit, Pranav Upadrashta, Alex Cloninger
We study a class of distributionally robust optimization (DRO) problems for the statistical risk problem, formulated as minimax problems over the product of a Euclidean space and a…
Resistance Distance and Linearized Optimal Transport on Graphs
Sawyer Robertson, Zhengchao Wan, Alexander Cloninger
We study the linearization of a discrete transportation distance between probability distributions on finite weighted graphs originally due to Maas (``Gradient flows of the entropy…
On a Generalization of Wasserstein Distance and the Beckmann Problem to Connection Graphs
Sawyer Robertson, Dhruv Kohli, Gal Mishne +1
We propose a model of optimal parallel transport between vector fields on a connection graph, which consists of a weighted graph along with a map from its edges to an orthogonal gr…