  We study offline recommender learning from explicit rating feedback in the
presence of selection bias. A current promising solution for the bias is the
inverse propensity score (IPS) estimation. However, the performance of existing
propensity-based methods can suffer significantly from the propensity
estimation bias. In fact, most of the previous IPS-based methods require some
amount of missing-completely-at-random (MCAR) data to accurately estimate the
propensity. This leads to a critical self-contradiction; IPS is ineffective
without MCAR data, even though it originally aims to learn recommenders from
only missing-not-at-random feedback. To resolve this propensity contradiction,
we derive a propensity-independent generalization error bound and propose a
novel algorithm to minimize the theoretical bound via adversarial learning. Our
theory and algorithm do not require a propensity estimation procedure, thereby
leading to a well-performing rating predictor without the true propensity
information. Extensive experiments demonstrate that the proposed approach is
superior to a range of existing methods both in rating prediction and ranking
metrics in practical settings without MCAR data.
