## 5 Discussion  
### Evaluation  
The approach that has been followed to solve the optimization problem for provider fairness in terms of coverage and diversity finds a heuristic solution to the problem that, according to the results, is very close to the optimal solution as it is very close to the results of the baseline recommender system that does not pose any constraint for coverage or diversity and hence acts as an upper bound for the proposed solution. Concerning the comparison of our results to other studies, only [PERSON] et al. [7] dealt with the same problem of provider fairness in terms of user coverage and diversity. The results of the proposed algorithm are similar to the experimental results in the aforementioned work, meaning that as diversity and coverage requirements increase, the total predicted rating of the recommended items tends to drop, while diversity constraints have a larger impact to the total rating. Moreover, our approach shows smaller deviation from the baseline solution, which poses the upper bound on the total predicted rating. Of course, this is not a safe inference as the solution of [7] does not clearly describes neither the preprocessing that took place nor the hyperparameters that have been used. In general, the advantage of treating the recommendation problem as a constraint optimization problem is that it ensures those certain criteria (the constraints) will be fulfilled. Of course, the constraints should be defined, also taking into consideration the tradeoff between the constraint requirements and the user preferences. This means that if the constraints are too stringent the relevance of the recommended items with the user may be critically low. Therefore, recommender system operators should always evaluate and update their requirements. Consequently, the proposed approach or a similar optimization approach with constraints for equal representation of providers or other stakeholder groups can be used in order to soften \"The winner takes it all phenomenon\" [26], in which the most significant providers (or groups of providers) have huge advantage over the others. This is because the optimization algorithm would secure at least a certain target of exposure (coverage, diversity, or any other metric) for all groups, if such a solution existed. Moreover, the proposed approach can also ensure that minority item providers will be protected as they would be guaranteed at least a certain amount of coverage and diversity. Additionally, with a similar approach, exposure and visibility for minority groups can also be achieved. However, the literature-based definition of the problem as an optimization one [7], poses several limitations. Firstly, it does not take into account the position of an item in the recommendation list. This is problematic because in most cases the position of the items in the user's list of recommendations plays a vital role in users' behavior, especially when the recommended items are numerous. For instance, a user may pay attention to the top few recommendations but not to the bottom ones. Another limitation of the problem definition at hand is that the definition of diversity fails to capture the dissimilarity among users to whom an item is recommended. Instead, it is observed that the most recommended items of a provider influence the diversity significantly more than the dissimilarity among the users to whom an item is recommended, and this fact is exploited by the heuristic approach that has been developed. To make this weakness more evident, we tried to approach the item's diversity as defined in the literature, by supposing that the dissimilarity of two different users is fixed and equals the average dissimilarity between two different users.