We study a novel variant of the domain adaptation problem, in which the loss
function on test data changes due to dependencies on prior predictions. One
important instance of this problem area occurs in settings where it is more costly
to make a new error than to repeat a previous error. We propose several methods for
learning effectively in this setting, and test them empirically on the real-world
tasks of malicious URL classiﬁcation and adversarial advertisement detection.