Information Retrieval (IR) and Recommender Systems (RS) tasks are moving from computing a ranking of final results based on a single metric to multi-objective problems. Solving these problems leads to a set of Pareto-optimal solutions, known as Pareto frontier, in which no objective can be further improved without hurting the others. In principle, all the points on the Pareto frontier are potential candidates to represent the best model selected with respect to the combination of two, or more, metrics. To our knowledge, there are no well-recognized strategies to decide which point should be selected on the frontier. In this paper, we propose a novel, post-hoc, theoretically-justified technique, named "Population Distance from Utopia" (PDU), to identify and select the one-best Pareto-optimal solution from the frontier. In detail, PDU analyzes the distribution of the points by investigating how far each point is from its utopia point (the ideal performance for the objectives). The possibility of considering fine-grained utopia points allows PDU to select solutions tailored to individual user preferences, a novel feature we call "calibration". We compare PDU against existing state-of-the-art strategies through extensive experiments on tasks from both IR and RS. Experimental results show that PDU and combined with calibration notably impact the solution selection. Furthermore, the results show that the proposed framework selects a solution in a principled way, irrespective of its position on the frontier, thus overcoming the limits of other strategies.

翻译：信息检索（IR）与推荐系统（RS）任务正从基于单一指标的结果排序向多目标问题求解演进。这类问题的求解会产生一组帕累托最优解——即帕累托前沿，其中无法在不损害其他目标的前提下进一步改进任何单一目标。理论上，帕累托前沿上的所有点都是基于两个或多个指标组合选取最佳模型的潜在候选方案。据我们所知，目前尚未建立公认的确定前沿最优选择点的策略。本文提出一种新颖的、具有理论支撑的事后选择技术——"群体与乌托邦距离"（Population Distance from Utopia, PDU），用于从前沿中识别并选取唯一最优帕累托解。具体而言，PDU通过分析各点与乌托邦点（各目标的理想性能）的距离分布来实现选择。考虑细粒度乌托邦点的可能性使PDU能够针对个体用户偏好定制解，我们将这一新特性称为"校准"。通过在信息检索与推荐系统任务上的广泛实验，我们将PDU与现有最优策略进行对比。实验结果表明，结合校准机制的PDU显著影响解的选择过程。此外，研究结果证实该框架无论前沿位置如何都能以原则性方式选取解，从而克服了其他策略的局限性。