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.
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