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.
Summing fromk= 0tok=n−1yields F(µ 0)−F(µ n)≥ τ √β 2 n−1X k=0 ∥(H2 µk +βI d×d)− 1 2 ∇µF(µ k)∥2 L2 µk
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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.