Machine Learning (ML) for information security (InfoSec) utilizes distinct data types and formats which require different treatments during optimization/training on raw data. In this paper, we implement a malicious/benign URL predictor based on a transformer architecture that is trained from scratch. We show that in contrast to conventional natural language processing (NLP) transformers, this model requires a different training approach to work well. Specifically, we show that 1) pre-training on a massive corpus of unlabeled URL data for an auto-regressive task does not readily transfer to malicious/benign prediction but 2) that using an auxiliary auto-regressive loss improves performance when training from scratch. We introduce a method for mixed objective optimization, which dynamically balances contributions from both loss terms so that neither one of them dominates. We show that this method yields performance comparable to that of several top-performing benchmark classifiers.