Minimax Least-Square Policy Iteration for Cost-Aware Defense of Traffic Routing against Unknown Threats

Dynamic routing is one of the representative control scheme in transportation, production lines, and data transmission. In the modern context of connectivity and autonomy, routing decisions are potentially vulnerable to malicious attacks. In this paper, we consider the dynamic routing problem over parallel traffic links in the face of such threats. An attacker is capable of increasing or destabilizing traffic queues by strategic manipulating the nominally optimal routing decisions. A defender is capable of securing the correct routing decision. Attacking and defensive actions induce technological costs. The defender has no prior information about the attacker's strategy. We develop an least-square policy iteration algorithm for the defender to compute a cost-aware and threat-adaptive defensive strategy. The policy evaluation step computes a weight vector that minimizes the sampled temporal-difference error. We derive a concrete theoretical upper bound on the evaluation error based on the theory of value function approximation. The policy improvement step solves a minimax problem and thus iteratively computes the Markov perfect equilibrium of the security game. We also discuss the training error of the entire policy iteration process.