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Domain shifts in the training data are common in practical applications ofmachine learning; they occur for instance when the data is coming fromdifferent sources. Ideally, a ML model should work well independently of theseshifts, for example, by learning a domain-invariant representation. However,common ML losses do not give strong guarantees on how consistently the ML modelperforms for different domains, in particular, whether the model performs wellon a domain at the expense of its performance on another domain. In this paper,we build new theoretical foundations for this problem, by contributing a set ofmathematical relations between classical losses for supervised ML and theWasserstein distance in joint space (i.e. representation and output space). Weshow that classification or regression losses, when combined with a GAN-typediscriminator between domains, form an upper-bound to the true Wassersteindistance between domains. This implies a more invariant representation and alsomore stable prediction performance across domains. Theoretical results arecorroborated empirically on several image datasets. Our proposed approachsystematically produces the highest minimum classification accuracy acrossdomains, and the most invariant representation.

Learning Domain Invariant Representations by Joint Wasserstein Distance Minimization