Learning-Based DoS Attack Power Allocation in Multiprocess Systems

We study the denial-of-service (DoS) attack power allocation optimization in a multiprocess cyber-physical system (CPS), where sensors observe different dynamic processes and send the local estimated states to a remote estimator through wireless channels, while a DoS attacker allocates its attack power on different channels as interference to reduce the wireless transmission rates, and thus degrading the estimation accuracy of the remote estimator. We consider two attack optimization problems. One is to maximize the average estimation error of different processes, and the other is to maximize the minimal one. We formulate these problems as Markov decision processes (MDPs). Unlike the majority of existing works where the attacker is assumed to have complete knowledge of the CPS, we consider an attacker with no prior knowledge of the wireless channel model and the sensor information. To address this uncertainty issue and the curse of dimensionality, we provide a learning-based attack power allocation algorithm stemming from the double deep Q-network (DDQN) method. First, with a defined partial order, the maximal elements of the action space are determined. By investigating the characteristic of the MDP, we prove that the optimal attack allocations of both problems belong to the set of these elements. This property reduces the entire action space to a smaller subset and speeds up the learning algorithm. In addition, to further improve the data efficiency and learning performance, we propose two enhanced attack power allocation algorithms which add two auxiliary tasks of MDP transition estimation inspired by model-based reinforcement learning, i.e., the next state prediction and the current action estimation. Experimental results demonstrate the versatility and efficiency of the proposed algorithms in different system settings compared with other algorithms, such as the conventional value iteration, double Q-learning, and deep Q-network.