  Unsupervised domain adaptation (UDA) adapts a model from a labeled source
domain to an unlabeled target domain in a one-off way. Though widely applied,
UDA faces a great challenge whenever the distribution shift between the source
and the target is large. Gradual domain adaptation (GDA) mitigates this
limitation by using intermediate domains to gradually adapt from the source to
the target domain. In this work, we first theoretically analyze gradual
self-training, a popular GDA algorithm, and provide a significantly improved
generalization bound compared with Kumar et al. (2020). Our theoretical
analysis leads to an interesting insight: to minimize the generalization error
on the target domain, the sequence of intermediate domains should be placed
uniformly along the Wasserstein geodesic between the source and target domains.
The insight is particularly useful under the situation where intermediate
domains are missing or scarce, which is often the case in real-world
applications. Based on the insight, we propose $\textbf{G}$enerative Gradual
D$\textbf{O}$main $\textbf{A}$daptation with Optimal $\textbf{T}$ransport
(GOAT), an algorithmic framework that can generate intermediate domains in a
data-dependent way. More concretely, we first generate intermediate domains
along the Wasserstein geodesic between two given consecutive domains in a
feature space, then apply gradual self-training to adapt the source-trained
classifier to the target along the sequence of intermediate domains.
Empirically, we demonstrate that our GOAT framework can improve the performance
of standard GDA when the given intermediate domains are scarce, significantly
broadening the real-world application scenarios of GDA. Our code is available
at https://github.com/yifei-he/GOAT.
