  As machine learning models are deployed ever more broadly, it becomes
increasingly important that they are not only able to perform well on their
training distribution, but also yield accurate predictions when confronted with
distribution shift. The Distributionally Robust Optimization (DRO) framework
proposes to address this issue by training models to minimize their expected
risk under a collection of distributions, to imitate test-time shifts. This is
most commonly achieved by instance-level re-weighting of the training objective
to emulate the likelihood ratio with possible test distributions, which allows
for estimating their empirical risk via importance sampling (assuming that they
are subpopulations of the training distribution). However, re-weighting schemes
in the literature are usually limited due to the difficulty of keeping the
optimization problem tractable and the complexity of enforcing normalization
constraints. In this paper, we show that three simple ideas -- mini-batch level
normalization, a KL penalty and simultaneous gradient updates -- allow us to
train models with DRO using a broader class of parametric likelihood ratios. In
a series of experiments on both image and text classification benchmarks, we
find that models trained with the resulting parametric adversaries are
consistently more robust to subpopulation shifts when compared to other DRO
approaches, and that the method performs reliably well with little
hyper-parameter tuning. Code to reproduce our experiments can be found at
https://github.com/pmichel31415/P-DRO.
