One of the most challenging recommendation tasks is recommending to a new, previously unseen user. This is known as the 'user cold start' problem. Assuming certain features or attributes of users are known, one approach for handling new users is to initially model them based on their features. Motivated by an ad targeting application, this paper describes an extreme online recommendation setting where the cold start problem is perpetual. Every user is encountered by the system just once, receives a recommendation, and either consumes or ignores it, registering a binary reward. We introduce One-pass Factorization of Feature Sets, OFF-Set, a novel recommendation algorithm based on Latent Factor analysis, which models users by mapping their features to a latent space. Furthermore, OFF-Set is able to model non-linear interactions between pairs of features. OFF-Set is designed for purely online recommendation, performing lightweight updates of its model per each recommendation-reward observation. We evaluate OFF-Set against several state of the art baselines, and demonstrate its superiority on real ad-targeting data.