  Domain adaptation aims to transfer the knowledge learned on (data-rich)
source domains to (low-resource) target domains, and a popular method is
invariant representation learning, which matches and aligns the data
distributions on the feature space. Although this method is studied extensively
and applied on classification and regression problems, its adoption on ranking
problems is sporadic, and the few existing implementations lack theoretical
justifications. This paper revisits invariant representation learning for
ranking. Upon reviewing prior work, we found that they implement what we call
item-level alignment, which aligns the distributions of the items being ranked
from all lists in aggregate but ignores their list structure. However, the list
structure should be leveraged, because it is intrinsic to ranking problems
where the data and the metrics are defined and computed on lists, not the items
by themselves. To close this discrepancy, we propose list-level alignment --
learning domain-invariant representations at the higher level of lists. The
benefits are twofold: it leads to the first domain adaptation generalization
bound for ranking, in turn providing theoretical support for the proposed
method, and it achieves better empirical transfer performance for unsupervised
domain adaptation on ranking tasks, including passage reranking.
