A Regularizing Optimal Transport with f-Divergences Name f (v) f

The primal and dual are related by the Lagrangian L (,',), L ( ',,)= E We proceed to proofs of the theorems stated in Section 4. Assumption NTK, the regularization parameter, and it may also depend indirectly on the bound R . Theorem 4.2 follows immediately from Lemmas B.1 and B.2. Theorem The following result follows from Proposition E.4 and E.5 of of Luise et al. Interestingly, the rate of estimation of the Sinkhorn plan breaks the curse of dimensionality. B.2 Log-concavity of Sinkhorn Factor The optimal entropy regularized Sinkhorn plan is given by The optimal potentials satisfy fixed point equations. Using this result, one can prove the following lemma.