Domain adaptation (DA) benefits from the rigorous theoretical works that
study its insightful characteristics and various aspects, e.g., learning
domain-invariant representations and its trade-off. However, it seems not the
case for the multiple source DA and domain generalization (DG) settings which
are remarkably more complicated and sophisticated due to the involvement of
multiple source domains and potential unavailability of target domain during
training. In this paper, we develop novel upper-bounds for the target general
loss which appeal to us to define two kinds of domain-invariant
representations. We further study the pros and cons as well as the trade-offs
of enforcing learning each domain-invariant representation. Finally, we conduct
experiments to inspect the trade-off of these representations for offering
practical hints regarding how to use them in practice and explore other
interesting properties of our developed theory.

本研究探讨了多源领域自适应和领域泛化设置中的目标通用损失的上界和两种领域不变表示的定义，并研究了强制学习每个领域不变表示的优缺点和权衡，并通过实验来检查这些表示的权衡，探索了我们所开发的理论的其他有趣特性。