  We study the robust quickest change detection under unknown pre- and
post-change distributions. To deal with uncertainties in the data-generating
distributions, we formulate two data-driven ambiguity sets based on the
Wasserstein distance, without any parametric assumptions. The minimax robust
test is constructed as the CUSUM test under least favorable distributions, a
representative pair of distributions in the ambiguity sets. We show that the
minimax robust test can be obtained in a tractable way and is asymptotically
optimal. We investigate the effectiveness of the proposed robust test over
existing methods, including the generalized likelihood ratio test and the
robust test under KL divergence based ambiguity sets.
