P-MMF: Provider Max-min Fairness Re-ranking in Recommender System

In this paper, we address the issue of recommending fairly from the aspect of providers, which has become increasingly essential in multistakeholder recommender systems. Existing studies on provider fairness usually focused on designing proportion fairness (PF) metrics that first consider systematic fairness. However, sociological researches show that to make the market more stable, max-min fairness (MMF) is a better metric. The main reason is that MMF aims to improve the utility of the worst ones preferentially, guiding the system to support the providers in weak market positions. When applying MMF to recommender systems, how to balance user preferences and provider fairness in an online recommendation scenario is still a challenging problem. In this paper, we proposed an online re-ranking model named Provider Max-min Fairness Re-ranking (P-MMF) to tackle the problem. Specifically, P-MMF formulates provider fair recommendation as a resource allocation problem, where the exposure slots are considered the resources to be allocated to providers and the max-min fairness is used as the regularizer during the process. We show that the problem can be further represented as a regularized online optimizing problem and solved efficiently in its dual space. During the online re-ranking phase, a momentum gradient descent method is designed to conduct the dynamic re-ranking. Theoretical analysis showed that the regret of P-MMF can be bounded. Experimental results on four public recommender datasets demonstrated that P-MMF can outperformed the state-of-the-art baselines. Experimental results also show that P-MMF can retain small computationally costs on a corpus with the large number of items.