Adversarial Linear Quadratic Regulator under Falsified Actions

Reinforcement learning (RL) has been widely employed in communications, in the areas of interference management, resource allocation, signal detection, and power control, etc. Nevertheless, RL is vulnerable under various malicious attacks, such as adversarial examples and privacy intrusions. In this paper, a falsification attack on the agent actions in a scalar linear quadratic regulator (LQR) system is studied. This adversarial problem is formulated as a novel dynamic game by introducing an adversarial belief, and subgame perfect equilibria (SPEs) are characterized under different adversarial constraints. Numerical experiments show the impact of strategic interactions and justify the theoretic results.