  A deployed question answering (QA) model can easily fail when the test data
has a distribution shift compared to the training data. Robustness tuning (RT)
methods have been widely studied to enhance model robustness against
distribution shifts before model deployment. However, can we improve a model
after deployment? To answer this question, we evaluate test-time adaptation
(TTA) to improve a model after deployment. We first introduce COLDQA, a unified
evaluation benchmark for robust QA against text corruption and changes in
language and domain. We then evaluate previous TTA methods on COLDQA and
compare them to RT methods. We also propose a novel TTA method called online
imitation learning (OIL). Through extensive experiments, we find that TTA is
comparable to RT methods, and applying TTA after RT can significantly boost the
performance on COLDQA. Our proposed OIL improves TTA to be more robust to
variation in hyper-parameters and test distributions over time.
