Pareto Optimality for Fairness-constrained Collaborative Filtering

The well-known collaborative filtering (CF) models typically optimize a single objective summed over all historical user-item interactions. Due to inevitable imbalances and biases in real-world data, they may develop a policy that unfairly discriminates against certain subgroups with low sample frequencies. To balance overall recommendation performance and fairness, prevalent solutions apply fairness constraints or regularizations to enforce equality of certain performance across different subgroups. However, simply enforcing equality of performance may lead to large performance degradation of those advantaged subgroups. To address this issue, we formulate a constrained Multi-Objective Optimization (MOO) problem. In contrast to the single objective, we treat the performance of each subgroup equivalently as an objective. This ensures that the imbalanced subgroup sample frequency does not affect the gradient information. We further propose fairness constraints to limit the search space to obtain more balanced solutions. To solve the constrained MOO problem, a gradient-based constrained MOO algorithm is proposed to seek a proper Pareto optimal solution for the performance trade-off. Extensive experiments on synthetic and real-world datasets show that our approach could help improve the recommendation accuracy of disadvantaged groups, while not damaging the overall performance.