Active Anomaly Detection with Switching Cost

TL;DR

This paper addresses active anomaly detection among multiple processes, incorporating switching costs into the decision-making process, and proposes low-complexity policies that are asymptotically optimal or order optimal under different cost regimes.

Contribution

It introduces a novel active inference strategy that accounts for switching costs, extending previous work focused solely on observation costs.

Findings

Proposed policies are asymptotically optimal when switching costs are negligible.

Policies are order optimal when switching costs are comparable to observation costs.

Simulation results show strong finite-sample performance.

Abstract

The problem of detecting a single anomalous process among multiple independent processes is considered. Under a constraint on the number of processes that can be probed simultaneously, the decision maker should decide which processes to probe at each time and when to terminate the probing. Compared with previous work considering only the observation costs, the switching costs of switchings across processes also need to be taken into account in many practical scenarios. The objective is an active inference strategy that minimizes the Bayesian risk taking into account of the sample complexity, switching cost, as well as detection errors. Based on the framework of sequential design of experiments, we propose a low-complexity, low-switching deterministic policy for two scenarios where the total switching cost is negligible and the total switching cost is comparable to the total observation cost. We show that the proposed algorithm is asymptotically optimal in the former scenario and is order optimal in the latter scenario. Simulation results demonstrate strong performance in the finite regime for both scenarios.