Convergence Analysis of the Wasserstein Proximal Algorithm beyond Geodesic Convexity
The Wasserstein proximal algorithm provides an unbiased and dimension-free linear convergence rate for minimizing functionals under a Polyak-Łojasiewicz (PL) type inequality, even when the objective function lacks geodesic convexity. This offers a new training scheme for two-layer neural networks in the mean-field regime, proving faster than noisy gradient descent methods.