Taming the Adversary: A Cost-to-Disturbance Ratio Approach to Adversarial Reinforcement Learning

Reinforcement learning (RL) policies trained in simulation often degrade once deployed on real systems, where the controller must reject external disturbances that were never encountered in simulation. Robust RL addresses this by exposing the controller to perturbations while it learns, through domain randomization, adversarial minimax formulations, or probabilistic mixtures of protagonist and adversarial behavior. However, an unregulated disturbance mechanism destabilizes training and often collapses nominal performance relative to standard, non-robust methods. We propose cost-to-disturbance ratio adversarial training (CoDRA), a framework that expresses the controller--adversary trade-off as a ratio of accumulated cost to accumulated squared disturbance norm, and optimizes it through a self-normalized actor--critic update. In this algorithm, each value term is scaled by a stop-gradient normalization constant computed from the current batch. This moderates the adversary's incentive without altering the controller's own update, and requires neither an explicit disturbance penalty nor an auxiliary trade-off parameter. We evaluate CoDRA on two MuJoCo pendulum environments under force and mass sweeps. On InvertedDoublePendulum, CoDRA attains the lowest cost at every force level, including a force outside the range seen during training, and in all but one cell of the mass grid, whereas its advantage is less pronounced on the milder InvertedPendulum.