Strategic Planning of Stealthy Backdoor Attacks in Markov Decision Processes

This paper investigates backdoor attack planning in stochastic control systems modeled as Markov Decision Processes (MDPs). In a backdoor attack, the adversary provides a control policy that behaves well in the original MDP to pass the testing phase. However, when such a policy is deployed with a trigger policy, which perturbs the system dynamics at runtime, it optimizes the attacker's objective instead. To solve jointly the control policy and its trigger, we formulate the attack planning problem as a constrained optimal planning problem in an MDP with augmented state space, with the objective to maximize the attacker's total rewards in the system with an activated trigger, subject to the constraint that the control policy is near optimal in the original MDP. We then introduce a gradient-based optimization method to solve the optimal backdoor attack policy as a pair of coordinated control and trigger policies. Experimental results from a case study validate the effectiveness of our approach in achieving stealthy backdoor attacks.