Abstract: BERT-era question answering systems have recently achieved impressive performance on several question-answering (QA) tasks. These systems are based on representations that have been pre-trained on self-supervised tasks such as word masking and sentence entailment, using massive amounts of data. Nevertheless, additional pre-training closer to the end-task, such as training on synthetic QA pairs, has been shown to improve performance. While recent work has considered augmenting labelled data and leveraging large unlabelled datasets to generate synthetic QA data, directly adapting to target data has received little attention. In this paper we investigate the iterative generation of synthetic QA pairs as a way to realize unsupervised self adaptation. Motivated by the success of the roundtrip consistency method for filtering generated QA pairs, we present iterative generalizations of the approach, which maximize an approximation of a lower bound on the probability of the adaptation data. By adapting on synthetic QA pairs generated on the target data, our method is able to improve QA systems significantly, using an order of magnitude less synthetic data and training computation than existing augmentation approaches.