Domain adaptation aims to transfer the knowledge acquired by models trained on (data-rich) source domains to (low-resource) target domains, for which a popular method is invariant representation learning. While they have been studied extensively for classification and regression problems, how they apply to ranking problems, where the data and metrics have a list structure, is not well understood. Theoretically, we establish a domain adaptation generalization bound for ranking under listwise metrics such as MRR and NDCG. The bound suggests an adaptation method via learning list-level domain-invariant feature representations, whose benefits are empirically demonstrated by unsupervised domain adaptation experiments on real-world ranking tasks, including passage reranking. A key message is that for domain adaptation, the representations should be analyzed at the same level at which the metric is computed, as we show that learning invariant representations at the list level is most effective for adaptation on ranking problems.
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