Efficient and Fair Item Coverage in Recommender Systems

We study the design of recommender systems under the constraint of item coverage. An item is covered if it is recommended at least to a certain number of users. This situation arises in settings where the items to be recommended stem from different entities such as owners, producers or advertisers with whom the recommendation engine has come into agreement about item promotion through recommendation, in exchange for some payment. It is therefore important to issue recommendations with breadth, in the sense that each item reaches a sufficiently large portion of the user base through recommendation. This constraint drastically changes the recommendation problem since now the lists of items to be recommended to different users become coupled. We formulate and study the recommendation problem under the item coverage constraint, with the goal of minimizing the cost of deviation from a nominal recommender system which does not cater for item coverage. We show that the linear-programming relaxation of the problem gives the optimal integral solution, and we also propose a low-complexity heuristic algorithm to solve large instances of the problem. Further, we study the problem of guaranteeing item coverage while making the incurred cost of deviation as balanced as possible across items (and therefore across their owners) or across users. The plots in the numerical results section demonstrate and quantify the trade-off between recommendation accuracy and item coverage and that between cost imbalance across items and coverage.