  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.
