  Deep neural networks (DNNs) have shown their success as high-dimensional
function approximators in many applications; however, training DNNs can be
challenging in general. DNN training is commonly phrased as a stochastic
optimization problem whose challenges include non-convexity, non-smoothness,
insufficient regularization, and complicated data distributions. Hence, the
performance of DNNs on a given task depends crucially on tuning
hyperparameters, especially learning rates and regularization parameters. In
the absence of theoretical guidelines or prior experience on similar tasks,
this requires solving many training problems, which can be time-consuming and
demanding on computational resources. This can limit the applicability of DNNs
to problems with non-standard, complex, and scarce datasets, e.g., those
arising in many scientific applications. To remedy the challenges of DNN
training, we propose slimTrain, a stochastic optimization method for training
DNNs with reduced sensitivity to the choice hyperparameters and fast initial
convergence. The central idea of slimTrain is to exploit the separability
inherent in many DNN architectures; that is, we separate the DNN into a
nonlinear feature extractor followed by a linear model. This separability
allows us to leverage recent advances made for solving large-scale, linear,
ill-posed inverse problems. Crucially, for the linear weights, slimTrain does
not require a learning rate and automatically adapts the regularization
parameter. Since our method operates on mini-batches, its computational
overhead per iteration is modest. In our numerical experiments, slimTrain
outperforms existing DNN training methods with the recommended hyperparameter
settings and reduces the sensitivity of DNN training to the remaining
hyperparameters.
