  This paper is concerned with the optimal allocation of detection resources
(sensors) to mitigate multi-stage attacks, in the presence of the defender's
uncertainty in the 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 the attacker. Based on this modeling framework, 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 framework using a stochastic gridworld
example.
