  Domain generalization aims to learn a predictive model from multiple
different but related source tasks that can generalize well to a target task
without the need of accessing any target data. Existing domain generalization
methods ignore the relationship between tasks, implicitly assuming that all the
tasks are sampled from a stationary environment. Therefore, they can fail when
deployed in an evolving environment. To this end, we formulate and study the
\emph{evolving domain generalization} (EDG) scenario, which exploits not only
the source data but also their evolving pattern to generate a model for the
unseen task. Our theoretical result reveals the benefits of modeling the
relation between two consecutive tasks by learning a globally consistent
directional mapping function. In practice, our analysis also suggests solving
the DDG problem in a meta-learning manner, which leads to \emph{directional
prototypical network}, the first method for the DDG problem. Empirical
evaluation of both synthetic and real-world data sets validates the
effectiveness of our approach.
