Multiple-source adaptation theory and algorithms – addendum

In this note, we present some key results complementing a previous manuscript (Hoffman et al., Ann. Math. Artif. Intell. 89(3-4), 237–270, 2021) dealing with the problem of multiple-source adaptation, a key learning problem in applications. In particular, we extend the theoretical results presented for the probability model to the case where estimated distributions are used, first by giving a guarantee that depends on the Rényi divergence of the target distribution and the family of mixtures of estimated distributions, next by generalizing that to a result that only depends on the Rényi divergence with respect to the family of mixtures of the exact source distributions.