SupplementaryMaterial: RobustOptimalTransport withApplicationsinGenerativeModelingand DomainAdaptation 1 Proofs

Y The constraint P X,P Y Prob(X) states that P X and P Y are valid probability distributions. For brevity, we shall ignore explicitly stating it in the rest of the proof. The above equation is similar in spirit to the Kantrovich-Rubinstein duality. An important observation to note is that the above optimization only maximizes over a single discriminator function (as opposed to two functions in optimization (2)). Hence, it is easier to train it in large-scale deep learningproblemssuchasGANs.