  Training a deep neural network is an optimization problem with four main
ingredients: the design of the deep neural network, the per-sample loss
function, the population loss function, and the optimizer. However, methods
developed to compete in recent BraTS challenges tend to focus only on the
design of deep neural network architectures, while paying less attention to the
three other aspects. In this paper, we experimented with adopting the opposite
approach. We stuck to a generic and state-of-the-art 3D U-Net architecture and
experimented with a non-standard per-sample loss function, the generalized
Wasserstein Dice loss, a non-standard population loss function, corresponding
to distributionally robust optimization, and a non-standard optimizer, Ranger.
Those variations were selected specifically for the problem of multi-class
brain tumor segmentation. The generalized Wasserstein Dice loss is a per-sample
loss function that allows taking advantage of the hierarchical structure of the
tumor regions labeled in BraTS. Distributionally robust optimization is a
generalization of empirical risk minimization that accounts for the presence of
underrepresented subdomains in the training dataset. Ranger is a generalization
of the widely used Adam optimizer that is more stable with small batch size and
noisy labels. We found that each of those variations of the optimization of
deep neural networks for brain tumor segmentation leads to improvements in
terms of Dice scores and Hausdorff distances. With an ensemble of three deep
neural networks trained with various optimization procedures, we achieved
promising results on the validation dataset of the BraTS 2020 challenge. Our
ensemble ranked fourth out of the 693 registered teams for the segmentation
task of the BraTS 2020 challenge.
