  We consider a semi-supervised classification problem with non-stationary
label-shift in which we observe a labelled data set followed by a sequence of
unlabelled covariate vectors in which the marginal probabilities of the class
labels may change over time. Our objective is to predict the corresponding
class-label for each covariate vector, without ever observing the ground-truth
labels, beyond the initial labelled data set. Previous work has demonstrated
the potential of sophisticated variants of online gradient descent to perform
competitively with the optimal dynamic strategy (Bai et al. 2022). In this work
we explore an alternative approach grounded in statistical methods for adaptive
transfer learning. We demonstrate the merits of this alternative methodology by
establishing a high-probability regret bound on the test error at any given
individual test-time, which adapt automatically to the unknown dynamics of the
marginal label probabilities. Further more, we give bounds on the average
dynamic regret which match the average guarantees of the online learning
perspective for any given time interval.
