Abstract: Domain adaptation, transfer, multitask, meta, few-shots, representation, or lifelong learning … these are all important recent directions in ML that all touch at the core of what we might mean by ‘AI’. As these directions all concern learning in heterogeneous and ever-changing environments, they all share a central question: what information a data distribution may have about another, critically, in the context of a given estimation problem, e.g., classification, regression, bandits, etc. Our understanding of these problems is still…