  Typical adversarial-training-based unsupervised domain adaptation methods are
vulnerable when the source and target datasets are highly-complex or exhibit a
large discrepancy between their data distributions. Recently, several
Lipschitz-constraint-based methods have been explored. The satisfaction of
Lipschitz continuity guarantees a remarkable performance on a target domain.
However, they lack a mathematical analysis of why a Lipschitz constraint is
beneficial to unsupervised domain adaptation and usually perform poorly on
large-scale datasets. In this paper, we take the principle of utilizing a
Lipschitz constraint further by discussing how it affects the error bound of
unsupervised domain adaptation. A connection between them is built and an
illustration of how Lipschitzness reduces the error bound is presented. A
\textbf{local smooth discrepancy} is defined to measure Lipschitzness of a
target distribution in a pointwise way. When constructing a deep end-to-end
model, to ensure the effectiveness and stability of unsupervised domain
adaptation, three critical factors are considered in our proposed optimization
strategy, i.e., the sample amount of a target domain, dimension and batchsize
of samples. Experimental results demonstrate that our model performs well on
several standard benchmarks. Our ablation study shows that the sample amount of
a target domain, the dimension and batchsize of samples indeed greatly impact
Lipschitz-constraint-based methods' ability to handle large-scale datasets.
Code is available at https://github.com/CuthbertCai/SRDA.
