Resilient observation selection in adversarial settings

Monitoring large areas using sensors is fundamental in a number of applications, including electric power grid, traffic networks, and sensor-based pollution control systems. However, the number of sensors that can be deployed is often limited by financial or technological constraints. This problem is further complicated by the presence of strategic adversaries, who may disable some of the deployed sensors in order to impair the operator's ability to make predictions. Assuming that the operator employs a Gaussian-process-based regression model, we formulate the problem of attack-resilient sensor placement as the problem of selecting a subset from a set of possible observations, with the goal of minimizing the uncertainty of predictions. We show that both finding an optimal resilient subset and finding an optimal attack against a given subset are NP-hard problems. Since both the design and the attack problems are computationally complex, we propose efficient heuristic algorithms for solving them and present theoretical approximability results. Finally, we show that the proposed algorithms perform exceptionally well in practice using numerical results based on real-world datasets.