Anomaly Search Over Many Sequences With Switching Costs

This letter considers the quickest search problem to identify anomalies among large numbers of data streams. These streams can model, for example, disjoint regions monitored by a mobile robot. A particular challenge is a version of the problem in which the experimenter must suffer a cost each time the data stream being sampled changes, such as the time the robot must spend moving between regions. In this letter, we propose an algorithm which accounts for switching costs by varying a confidence threshold that governs when the algorithm switches to a new data stream. Our main contributions are easily computable approximations for both the optimal value of this threshold and the optimal value of the parameter that determines when a stream is flagged as an anomaly, using the Brownian motion approximations. Further, we empirically show (i) a uniform improvement for switching costs of interest and (ii) roughly equivalent performance for small switching costs when comparing to the closest available algorithm.