  Distributionally Robust Supervised Learning (DRSL) is necessary for building
reliable machine learning systems. When machine learning is deployed in the
real world, its performance can be significantly degraded because test data may
follow a different distribution from training data. DRSL with f-divergences
explicitly considers the worst-case distribution shift by minimizing the
adversarially reweighted training loss. In this paper, we analyze this DRSL,
focusing on the classification scenario. Since the DRSL is explicitly
formulated for a distribution shift scenario, we naturally expect it to give a
robust classifier that can aggressively handle shifted distributions. However,
surprisingly, we prove that the DRSL just ends up giving a classifier that
exactly fits the given training distribution, which is too pessimistic. This
pessimism comes from two sources: the particular losses used in classification
and the fact that the variety of distributions to which the DRSL tries to be
robust is too wide. Motivated by our analysis, we propose simple DRSL that
overcomes this pessimism and empirically demonstrate its effectiveness.
