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Information Retrieval (IR) and Recommender Systems (RS) tasks are moving fromcomputing a ranking of final results based on a single metric tomulti-objective problems. Solving these problems leads to a set ofPareto-optimal solutions, known as Pareto frontier, in which no objective canbe further improved without hurting the others. In principle, all the points onthe Pareto frontier are potential candidates to represent the best modelselected with respect to the combination of two, or more, metrics. To ourknowledge, there are no well-recognized strategies to decide which point shouldbe 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 thefrontier. In detail, PDU analyzes the distribution of the points byinvestigating how far each point is from its utopia point (the idealperformance for the objectives). The possibility of considering fine-grainedutopia points allows PDU to select solutions tailored to individual userpreferences, a novel feature we call "calibration". We compare PDU againstexisting state-of-the-art strategies through extensive experiments on tasksfrom both IR and RS. Experimental results show that PDU and combined withcalibration notably impact the solution selection. Furthermore, the resultsshow that the proposed framework selects a solution in a principled way,irrespective of its position on the frontier, thus overcoming the limits ofother strategies.

Post-hoc Selection of Pareto-Optimal Solutions in Search and Recommendation