  A two-sample hypothesis test is a statistical procedure used to determine
whether the distributions generating two samples are identical. We consider the
two-sample testing problem in a new scenario where the sample measurements (or
sample features) are inexpensive to access, but their group memberships (or
labels) are costly. To address the problem, we devise the first \emph{active
sequential two-sample testing framework} that not only sequentially but also
\emph{actively queries}. Our test statistic is a likelihood ratio where one
likelihood is found by maximization over all class priors, and the other is
provided by a probabilistic classification model. The classification model is
adaptively updated and used to predict where the (unlabelled) features have a
high dependency on labels; labeling the ``high-dependency'' features leads to
the increased power of the proposed testing framework. In theory, we provide
the proof that our framework produces an \emph{anytime-valid} $p$-value. In
addition, we characterize the proposed framework's gain in testing power by
analyzing the mutual information between the feature and label variables in
asymptotic and finite-sample scenarios. In practice, we introduce an
instantiation of our framework and evaluate it using several experiments; the
experiments on the synthetic, MNIST, and application-specific datasets
demonstrate that the testing power of the instantiated active sequential test
significantly increases while the Type I error is under control.
