  The interventional nature of recommendation has attracted increasing
attention in recent years. It particularly motivates researchers to formulate
learning and evaluating recommendation as causal inference and data
missing-not-at-random problems. However, few take seriously the consequence of
violating the critical assumption of overlapping, which we prove can
significantly threaten the validity and interpretation of the outcome. We find
a critical piece missing in the current understanding of information retrieval
(IR) systems: as interventions, recommendation not only affects the already
observed data, but it also interferes with the target domain (distribution) of
interest. We then rephrase optimizing recommendation as finding an intervention
that best transports the patterns it learns from the observed domain to its
intervention domain. Towards this end, we use domain transportation to
characterize the learning-intervention mechanism of recommendation. We design a
principled transportation-constraint risk minimization objective and convert it
to a two-player minimax game. We prove the consistency, generalization, and
excessive risk bounds for the proposed objective, and elaborate how they
compare to the current results. Finally, we carry out extensive real-data and
semi-synthetic experiments to demonstrate the advantage of our approach, and
launch online testing with a real-world IR system.
