Domain Adaptation (DA) or Transfer Learning concerns problems where the training data distribution is different from the test distribution. Many notions of distance or divergences between distributions have been proposed in the literature to address these problems, all resulting in separate algorithmic approaches. Are there unified algorithmic principles?
I plan to first overview the various families of divergences considered in the literature on DA and discuss their limitations. I will then discuss how some simple moduli of continuity between risk measures allow for a unified statistical and algorithmic take on DA. In particular, these so-called "moduli of transfer" lower-bound many of the classical divergences considered in the literature on DA, both for classification and regression problems, and can be shown to recover existing guarantees on DA. Moreover, they shed light on unified algorithmic principles via reductions to adaptive confidence sets.