  Most recommender systems optimize the model on observed interaction data,
which is affected by the previous exposure mechanism and exhibits many biases
like popularity bias. The loss functions, such as the mostly used pointwise
Binary Cross-Entropy and pairwise Bayesian Personalized Ranking, are not
designed to consider the biases in observed data. As a result, the model
optimized on the loss would inherit the data biases, or even worse, amplify the
biases. For example, a few popular items take up more and more exposure
opportunities, severely hurting the recommendation quality on niche items --
known as the notorious Mathew effect. In this work, we develop a new learning
paradigm named Cross Pairwise Ranking (CPR) that achieves unbiased
recommendation without knowing the exposure mechanism. Distinct from inverse
propensity scoring (IPS), we change the loss term of a sample -- we
innovatively sample multiple observed interactions once and form the loss as
the combination of their predictions. We prove in theory that this way offsets
the influence of user/item propensity on the learning, removing the influence
of data biases caused by the exposure mechanism. Advantageous to IPS, our
proposed CPR ensures unbiased learning for each training instance without the
need of setting the propensity scores. Experimental results demonstrate the
superiority of CPR over state-of-the-art debiasing solutions in both model
generalization and training efficiency. The codes are available at
https://github.com/Qcactus/CPR.
