  Concept shift is a prevailing problem in natural tasks like medical image
segmentation where samples usually come from different subpopulations with
variant correlations between features and labels. One common type of concept
shift in medical image segmentation is the "information imbalance" between
label-sparse samples with few (if any) segmentation labels and label-dense
samples with plentiful labeled pixels. Existing distributionally robust
algorithms have focused on adaptively truncating/down-weighting the "less
informative" (i.e., label-sparse in our context) samples. To exploit data
features of label-sparse samples more efficiently, we propose an adaptively
weighted online optimization algorithm -- AdaWAC -- to incorporate data
augmentation consistency regularization in sample reweighting. Our method
introduces a set of trainable weights to balance the supervised loss and
unsupervised consistency regularization of each sample separately. At the
saddle point of the underlying objective, the weights assign label-dense
samples to the supervised loss and label-sparse samples to the unsupervised
consistency regularization. We provide a convergence guarantee by recasting the
optimization as online mirror descent on a saddle point problem. Our empirical
results demonstrate that AdaWAC not only enhances the segmentation performance
and sample efficiency but also improves the robustness to concept shift on
various medical image segmentation tasks with different UNet-style backbones.
