One for All: Simultaneous Metric and Preference Learning over Multiple Users

This paper investigates simultaneous preference and metric learning from a crowd of respondents. A set of items represented by d -dimensional feature vectors and paired comparisons of the form item i is preferable to item j '' made by each user is given. Our model jointly learns a distance metric that characterizes the crowd's general measure of item similarities along with a latent ideal point for each user reflecting their individual preferences. This model has the flexibility to capture individual preferences, while enjoying a metric learning sample cost that is amortized over the crowd. We first study this problem in a noiseless, continuous response setting (i.e., responses equal to differences of item distances) to understand the fundamental limits of learning.