All transductive recommender systems are unable to make predictions for users who were not included in the training sample due to the process of learning user-specific embeddings. In this paper, we propose a new method for replacing identity-based user embeddings in existing sequential models with interaction-based user vectors trained purely on interaction sequences. Such vectors are composed of user interactions using GRU layers with adjusted dropout and maximum item sequence length. This approach is substantially more efficient and does not require retraining when new users appear. Extensive experiments on three open-source datasets demonstrate noticeable improvement in quality metrics for the most of selected state-of-the-art sequential recommender models.