  This paper is an extended version of [Burashnikova et al., 2021, arXiv:
2012.06910], where we proposed a theoretically supported sequential strategy
for training a large-scale Recommender System (RS) over implicit feedback,
mainly in the form of clicks. The proposed approach consists in minimizing
pairwise ranking loss over blocks of consecutive items constituted by a
sequence of non-clicked items followed by a clicked one for each user. We
present two variants of this strategy where model parameters are updated using
either the momentum method or a gradient-based approach. To prevent updating
the parameters for an abnormally high number of clicks over some targeted items
(mainly due to bots), we introduce an upper and a lower threshold on the number
of updates for each user. These thresholds are estimated over the distribution
of the number of blocks in the training set. They affect the decision of RS by
shifting the distribution of items that are shown to the users. Furthermore, we
provide a convergence analysis of both algorithms and demonstrate their
practical efficiency over six large-scale collections with respect to various
ranking measures.
