Deep preference learning for multiple criteria decision analysis

Abstract

We propose preference learning algorithms for inferring the parameters of a threshold-based sorting model from large sets of assignment examples. The introduced framework is adjusted to different scores originally used in Multiple Criteria Decision Analysis (MCDA). They include Ordered Weighted Average, an additive value function, the Choquet integral, a distance from the ideal and anti-ideal alternatives, and Net Flow Scores built on the results of outranking-based pairwise comparisons. As a concrete application of these models, we use Artificial Neural Networks with up to five hidden layers. Their components and architecture are designed to ensure high interpretability, which supports the models’ acceptance by domain experts. To learn the most favorable values of all parameters at once, we use a variant of a gradient descent optimization algorithm called AdamW. In this way, we make the MCDA methods suitable for handling vast, inconsistent information. The extensive experiments on various benchmark problems indicate that the introduced algorithms are competitive in predictive accuracy quantified in terms of Area Under Curve and the 0/1 loss. In this regard, some approaches outperform the state-of-the-art algorithms, including generalizations of logistic regression, mathematical programming, rule ensemble and tree induction algorithms, or dedicated heuristics.