  Distributionally robust optimization (DRO) provides a framework for training
machine learning models that are able to perform well on a collection of
related data distributions (the "uncertainty set"). This is done by solving a
min-max game: the model is trained to minimize its maximum expected loss among
all distributions in the uncertainty set. While careful design of the
uncertainty set is critical to the success of the DRO procedure, previous work
has been limited to relatively simple alternatives that keep the min-max
optimization problem exactly tractable, such as $f$-divergence balls. In this
paper, we argue instead for the use of neural generative models to characterize
the worst-case distribution, allowing for more flexible and problem-specific
selection of the uncertainty set. However, while simple conceptually, this
approach poses a number of implementation and optimization challenges. To
circumvent these issues, we propose a relaxation of the KL-constrained inner
maximization objective that makes the DRO problem more amenable to
gradient-based optimization of large scale generative models, and develop model
selection heuristics to guide hyper-parameter search. On both toy settings and
realistic NLP tasks, we find that the proposed approach yields models that are
more robust than comparable baselines.
