Introduces WSFN, a Newton-type method on Wasserstein space that escapes saddle points in polynomial time and achieves linear convergence to global minimizers under benign landscape assumptions.
Using the Taylor expansionlog(1 + x) = Θ(x)2, for small enoughx > 0, we see thatnout = ˜O(˜δ−1)
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From Saddle Points Toward Global Minima: A Newton-Type Method on Wasserstein Space
Introduces WSFN, a Newton-type method on Wasserstein space that escapes saddle points in polynomial time and achieves linear convergence to global minimizers under benign landscape assumptions.