  Recommender systems (RSs) employ user-item feedback, e.g., ratings, to match
customers to personalized lists of products. Approaches to top-k recommendation
mainly rely on Learning-To-Rank algorithms and, among them, the most widely
adopted is Bayesian Personalized Ranking (BPR), which bases on a pair-wise
optimization approach. Recently, BPR has been found vulnerable against
adversarial perturbations of its model parameters. Adversarial Personalized
Ranking (APR) mitigates this issue by robustifying BPR via an adversarial
training procedure. The empirical improvements of APR's accuracy performance on
BPR have led to its wide use in several recommender models. However, a key
overlooked aspect has been the beyond-accuracy performance of APR, i.e.,
novelty, coverage, and amplification of popularity bias, considering that
recent results suggest that BPR, the building block of APR, is sensitive to the
intensification of biases and reduction of recommendation novelty. In this
work, we model the learning characteristics of the BPR and APR optimization
frameworks to give mathematical evidence that, when the feedback data have a
tailed distribution, APR amplifies the popularity bias more than BPR due to an
unbalanced number of received positive updates from short-head items. Using
matrix factorization (MF), we empirically validate the theoretical results by
performing preliminary experiments on two public datasets to compare BPR-MF and
APR-MF performance on accuracy and beyond-accuracy metrics. The experimental
results consistently show the degradation of novelty and coverage measures and
a worrying amplification of bias.
