Optimizing Sensor Allocation Against Attackers With Uncertain Intentions: A Worst-Case Regret Minimization Approach

Haoxiang Ma, Shuo Han, Charles A. Kamhoua, Jie Fu

Abstract: This letter focuses on the optimal allocation of multi-stage attacks with the uncertainty in attacker’s intention. We model the attack planning problem using a Markov decision process and characterize the uncertainty in the attacker’s intention using a finite set of reward functions—each reward represents a type of attacker. Based on this modeling, we employ the paradigm of the worst-case absolute regret minimization from robust game theory and develop mixed-integer linear program (MILP) formulations for solving the worst-case regret minimizing sensor allocation strategies for two classes of attack-defend interactions: one where the defender and attacker engage in a zero-sum game and another where they engage in a non-zero-sum game. We demonstrate the effectiveness of our algorithm using a stochastic gridworld example.