  Recent work has shown the importance of adaptation of broad-coverage
contextualised embedding models on the domain of the target task of interest.
Current self-supervised adaptation methods are simplistic, as the training
signal comes from a small percentage of \emph{randomly} masked-out tokens. In
this paper, we show that careful masking strategies can bridge the knowledge
gap of masked language models (MLMs) about the domains more effectively by
allocating self-supervision where it is needed. Furthermore, we propose an
effective training strategy by adversarially masking out those tokens which are
harder to reconstruct by the underlying MLM. The adversarial objective leads to
a challenging combinatorial optimisation problem over \emph{subsets} of tokens,
which we tackle efficiently through relaxation to a variational lowerbound and
dynamic programming. On six unsupervised domain adaptation tasks involving
named entity recognition, our method strongly outperforms the random masking
strategy and achieves up to +1.64 F1 score improvements.
