  We study the robustness of active learning (AL) algorithms against prior
misspecification: whether an algorithm achieves similar performance using a
perturbed prior as compared to using the true prior. In both the average and
worst cases of the maximum coverage setting, we prove that all
$\alpha$-approximate algorithms are robust (i.e., near $\alpha$-approximate) if
the utility is Lipschitz continuous in the prior. We further show that
robustness may not be achieved if the utility is non-Lipschitz. This suggests
we should use a Lipschitz utility for AL if robustness is required. For the
minimum cost setting, we can also obtain a robustness result for approximate AL
algorithms. Our results imply that many commonly used AL algorithms are robust
against perturbed priors. We then propose the use of a mixture prior to
alleviate the problem of prior misspecification. We analyze the robustness of
the uniform mixture prior and show experimentally that it performs reasonably
well in practice.
