On the use of Wasserstein distance in the distributional analysis of human decision making under uncertainty

Abstract The key contribution of this paper is a theoretical framework to analyse humans’ decision-making strategies under uncertainty, and more specifically how human subjects manage the trade-off between information gathering (exploration) reward seeking (exploitation) in particular active learning black-box optimization task. Humans’ decisions making according these two objectives can be modelled terms Pareto rationality. If decision set contains efficient (dominant) strategy, rational maker should always select dominant strategy over its dominated alternatives. A distance from frontier determines whether choice (Pareto) rational. element proposed analytical representation behavioural patterns learners as discrete probability distribution, histogram considered non-parametric estimate density function on real line. Thus, similarity users captured by their associated histograms. This maps problem characterization behaviour into space, whose elements are distributions, structured histograms, namely optimal transport-based Wasserstein distance. distributional analysis gives new insights search tasks deviations Since uncertainty one defining frontier, has been performed for three different quantification measures identify which better explains compliant patterns. Beside individual also enabled global computing WST barycenters performing k-means clustering.