Towards efficient pareto-optimal utility-fairness between groups in repeated rankings - Dinh, Phuong Mai; Le, Duc-Trong; Hoang, Tuan-Anh; Le, Dung Duy (Machine learning, 2025)
In this study, we tackle the problem of computing an expectation of ranking with the guarantee of the Pareto-optimal balance between (1) maximizing the utility of the consumers and (2) minimizing the exposure unfairness between item producers. Such a multi-objective optimization problem is typically solved using a scalarization method and linear programming on bi-stochastic matrices, representing the distribution of possible rankings of items. However, such an approach relies on Birkhoff-von Neumann (BvN) decomposition, which is computationally impractical for large-scale systems. To address this issue, we introduce a novel approach to the above problem by using the Expohedron—a permutahedron whose points represent all achievable exposures of items. On the Expohedron, we profile the Pareto curve, which captures the trade-off between group fairness and user utility by identifying a finite number of Pareto optimal solutions. We propose an efficient method by relaxing our optimization problem on the Expohedron’s circumscribed n -sphere, significantly improving the running time. Moreover, the approximate Pareto curve is asymptotically close to the natural Pareto optimal curve as the number of substantial solutions increases. Our methods are applicable with different ranking merits that are non-decreasing functions of item relevance. The effectiveness of our strategies is validated through experiments on both synthetic and real-world datasets.