Sequential Wasserstein Uncertainty Sets for Minimax Robust Online Change Detection

We consider the robust online change-point detection problem with unknown post-change distributions. An online sequence of non-parametric uncertainty sets are constructed for the underlying data distribution. We sequentially determine the least favorable distribution at every instance by framing the issue as an online convex optimization task. This least favorable distribution is then leveraged to calculate the log-likelihood ratio within our proposed online robust CUSUM (OR-CUSUM) detection statistic. We also present numerical findings to corroborate the effectiveness of the proposed OR-CUSUM test.