Optimal Sensor Deception to Deviate from an Allowed Itinerary

In this work, we study a class of deception planning problems in which an agent aims to alter a security monitoring system's sensor readings so as to disguise its adversarial itinerary as an allowed itinerary in the environment. The adversarial itinerary set and allowed itinerary set are captured by regular languages. To deviate without being detected, we investigate whether there exists a strategy for the agent to alter the sensor readings, with a minimal cost, such that for any of those paths it takes, the system thinks the agent took a path within the allowed itinerary. Our formulation assumes an offline sensor alteration where the agent determines the sensor alteration strategy and implement it, and then carry out any path in its deviation itinerary. We prove that the problem of solving the optimal sensor alteration is NP-hard, by a reduction from the directed multi-cut problem. Further, we present an exact algorithm based on integer linear programming and demonstrate the correctness and the efficacy of the algorithm in case studies.