  Domain generalization (DG) aims at learning a model on source domains to well
generalize on the unseen target domain. Although it has achieved great success,
most of existing methods require the label information for all training samples
in source domains, which is time-consuming and expensive in the real-world
application. In this paper, we resort to solving the semi-supervised domain
generalization (SSDG) task, where there are a few label information in each
source domain. To address the task, we first analyze the theory of the
multi-domain learning, which highlights that 1) mitigating the impact of domain
gap and 2) exploiting all samples to train the model can effectively reduce the
generalization error in each source domain so as to improve the quality of
pseudo-labels. According to the analysis, we propose MultiMatch, i.e.,
extending FixMatch to the multi-task learning framework, producing the
high-quality pseudo-label for SSDG. To be specific, we consider each training
domain as a single task (i.e., local task) and combine all training domains
together (i.e., global task) to train an extra task for the unseen test domain.
In the multi-task framework, we utilize the independent BN and classifier for
each task, which can effectively alleviate the interference from different
domains during pseudo-labeling. Also, most of parameters in the framework are
shared, which can be trained by all training samples sufficiently. Moreover, to
further boost the pseudo-label accuracy and the model's generalization, we fuse
the predictions from the global task and local task during training and
testing, respectively. A series of experiments validate the effectiveness of
the proposed method, and it outperforms the existing semi-supervised methods
and the SSDG method on several benchmark DG datasets.
