A reproducing kernel Hilbert space embedding yields a sample-only objective for solving continuum-marginal optimal transport without spatial discretization.
Mikami.Stochastic Optimal Transportation: Stochastic Control with Fixed Marginals
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Continuum-marginal optimal transport: a mesh-free kernel method
A reproducing kernel Hilbert space embedding yields a sample-only objective for solving continuum-marginal optimal transport without spatial discretization.