Dynamic Search on a Tree with Information-Directed Random Walk

摘要

The problem of detecting a few anomalous processes among a large number of data streams is considered. At each time, aggregated observations can be taken from a chosen subset of the processes, where the chosen subset conforms to a given tree structure. The random observations are drawn from a general distribution that may depend on the size of the chosen subset and the number of anomalous processes in the subset. We propose a sequential search strategy by devising an information-directed random walk (IRW) on the tree-structured observation hierarchy. The sample complexity of the IRW policy is shown to be asymptotically optimal with respect to the detection accuracy and order optimal with respect to the number of data streams. The results also find applications in noisy group testing, active learning, and channel coding with feedback.