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This paper investigates simultaneous preference and metric learning from acrowd of respondents. A set of items represented by $d$-dimensional featurevectors 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 metricthat characterizes the crowd's general measure of item similarities along witha latent ideal point for each user reflecting their individual preferences.This model has the flexibility to capture individual preferences, whileenjoying a metric learning sample cost that is amortized over the crowd. Wefirst study this problem in a noiseless, continuous response setting (i.e.,responses equal to differences of item distances) to understand the fundamentallimits of learning. Next, we establish prediction error guarantees for noisy,binary measurements such as may be collected from human respondents, and showhow the sample complexity improves when the underlying metric is low-rank.Finally, we establish recovery guarantees under assumptions on the responsedistribution. We demonstrate the performance of our model on both simulateddata and on a dataset of color preference judgements across a large number ofusers.

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