Title: Learning Listwise Domain-Invariant Representations for Ranking. Abstract: Domain adaptation aims to transfer models trained on data-rich domains to low-resource ones, for which a popular method is invariant representation learning. While they have been studied extensively for classification and regression problems, how they would apply to ranking problems, where the metrics and data follow a list structure, is not well understood. Theoretically, we establish a generalization bound for ranking problems under metrics including MRR and NDCG, leading to a method based on learning listwise invariant feature representations. The main novelty of our results is that they are tailored to the listwise approach of learning to rank: the invariant representations our method learns are for each list of items as a whole, instead of the individual items they contain. Our method is evaluated on the passage reranking task, where we adapt neural text rankers trained on a general domain to various specialized domains.