# Low-Cost Active Anomaly Detection with Switching Latency
### Related Work
When there is only one anomaly, minimizing the cumulative cost is equivalent to minimizing the sample size, because there is one and only one process incurring cost per unit time during the entire detection procedure. With multiple processes, however, minimizing the expected sample size based on the existing methods is no longer sufficient, since the abnormal process will stop incurring cost once its state is identified, which makes the cumulative per-unit-time cost incurred by all the anomalies change. The anomaly detection problem with the objective of minimizing the cumulative observation cost was formulated by [PERSON] and [PERSON] in [21], where they studied this problem with the restriction that across-processes switching is allowed only when the state of the probed process is declared. They focused on the scenario where the number of anomalies is unknown, developed optimal index algorithms and demonstrated its strong performance in terms of minimizing the expected cumulative observation cost through numerical simulations. Furthermore, they studied this problem in [22] without the switching restriction and developed index-type algorithms which had been proven to be asymptotically optimal as the error constraints approach zero. Then, [PERSON] [23] tackled a general nonlinear cost setting and developed an effective algorithm. However, these above studies do not consider the switching cost. Incorporating the switching cost into the objective function is motivated by lots of applications. For example, in many searching tasks, relocating the searching region using rescuing ships or air-crafts incurs a considerable cost in terms of energy or delay. Another example is medical diagnostics, where frequent and fast switching across drugs and medical procedures may carry high risk and side effects. Moreover, in power systems, switching different components to probe also incurs a certain amount of time delay and requires a switching cost. As for the AHT problem considering the switching cost, there are few studies in the literature. [PERSON] developed a modified Chernoff test (referred as Sluggish policy) in [24] and introduced a switching parameter \(\eta\) which determines the switching probability, which can significantly reduce the number of switchings. They claimed that Sluggish policy approaches the asymptotic performance of Chernoff test as \(\eta\to 0\). In our previous work [25; 26], we applied the AHT model to the single-target anomaly detection problem. We proposed a low-complexity deterministic policy (referred as DBS policy) which is shown to be asymptotically optimal and offers significant performance improvement in the finite regime. However, it should be noted that they all focused on the AHT problem from the perspective of minimizing the summation of the sample size and the switching cost and did not consider the expected cumulative cost. Thus, the anomaly detection problem with the objective of minimizing the expected cumulative cost considering the switching cost is first formulated and studied in this paper. In order to intuitively compare our work with the recent existing works, we show the differences in Table 1 according to the different objective functions and whether the switching costs are considered.