  Selecting or designing an appropriate domain adaptation algorithm for a given
problem remains challenging. This paper presents a Transformer model that can
provably approximate and opt for domain adaptation methods for a given dataset
in the in-context learning framework, where a foundation model performs new
tasks without updating its parameters at test time. Specifically, we prove that
Transformers can approximate instance-based and feature-based unsupervised
domain adaptation algorithms and automatically select an algorithm suited for a
given dataset. Numerical results indicate that in-context learning demonstrates
an adaptive domain adaptation surpassing existing methods.
