Sequential Outlier Hypothesis Testing under Universality Constraints

We revisit sequential outlier hypothesis testing and derive bounds on the achievable exponents. Specifically, the task of outlier hypothesis testing is to identify the set of outliers that are generated from an anomalous distribution among all observed sequences where most are generated from a nominal distribution. In the sequential setting, one obtains a sample from each sequence per unit time until a reliable decision could be made. We assume that the number of outliers is known while both the nominal and anomalous distributions are unknown. For the case of exactly one outlier, our bounds on the achievable exponents are tight, providing exact large deviations characterization of sequential tests and strengthening a previous result of Li, Nitinawarat and Veeravalli (2017). In particular, we propose a sequential test that has bounded average sample size and better theoretical performance than the fixed-length test, which could not be guaranteed by the corresponding sequential test of Li, Nitinawarat and Veeravalli (2017). Our results are also generalized to the case of multiple outliers.