Hyperparameter tuning remains a significant challenge for the training of deep neural networks (DNNs), requiring manual and/or time-intensive grid searches, increasing resource costs and presenting a barrier to the democratization of machine learning. The global initial learning rate for DNN training is particularly important. Several techniques have been proposed for automated learning rate tuning during training; however, they still require manual searching for the global initial learning rate. Though methods exist that do not require this initial selection, they suffer from poor performance. Here, we present ExpTest, a sophisticated method for initial learning rate searching and subsequent learning rate tuning for the training of DNNs. ExpTest draws on insights from linearized neural networks and the form of the loss curve, which we treat as a real-time signal upon which we perform hypothesis testing. We mathematically justify ExpTest and provide empirical support. ExpTest requires minimal overhead, is robust to hyperparameter choice, and achieves state-of-the-art performance on a variety of tasks and architectures, without initial learning rate selection or learning rate scheduling.