The evolution of social media users' behavior over time complicates user-level comparison tasks such as verification, classification, clustering, and ranking. As a result, naïve approaches may fail to generalize to new users or even to future observations of previously known users. In this paper, we propose a novel procedure to learn a mapping from short episodes of user activity on social media to a vector space in which the distance between points captures the similarity of the corresponding users' invariant features. We fit the model by optimizing a surrogate metric learning objective over a large corpus of unlabeled social media content. Once learned, the mapping may be applied to users not seen at training time and enables efficient comparisons of users in the resulting vector space. We present a comprehensive evaluation to validate the benefits of the proposed approach using data from Reddit, Twitter, and Wikipedia.