Post-Hoc selection of pareto-optimal solutions in search and recommendation

Information Retrieval (IR) and Recommender Systems (RSs) 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 IR and RSs. 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. PDU considers fine-grained utopia points, and measures how far each point is from its utopia point, allowing to select solutions tailored to user preferences, a novel feature we call "calibration". We compare PDU against state-of-the-art strategies through extensive experiments on tasks from both IR and RS, showing that PDU combined with calibration notably impacts the solution selection.