  Existing domain adaptation methods tend to treat every domain equally and
align them all perfectly. Such uniform alignment ignores topological structures
among different domains; therefore it may be beneficial for nearby domains, but
not necessarily for distant domains. In this work, we relax such uniform
alignment by using a domain graph to encode domain adjacency, e.g., a graph of
states in the US with each state as a domain and each edge indicating
adjacency, thereby allowing domains to align flexibly based on the graph
structure. We generalize the existing adversarial learning framework with a
novel graph discriminator using encoding-conditioned graph embeddings.
Theoretical analysis shows that at equilibrium, our method recovers classic
domain adaptation when the graph is a clique, and achieves non-trivial
alignment for other types of graphs. Empirical results show that our approach
successfully generalizes uniform alignment, naturally incorporates domain
information represented by graphs, and improves upon existing domain adaptation
methods on both synthetic and real-world datasets. Code will soon be available
at https://github.com/Wang-ML-Lab/GRDA.
