Adversarially Robust Stability Certificates can be Sample-Efficient
This work addresses safety-critical systems by providing sample-efficient adversarial robustness, but it is incremental as it builds on robust control and adversarial learning frameworks.
The paper tackles the problem of learning adversarially robust stability certificates for unknown nonlinear dynamical systems to bridge the simulation-to-reality gap in safety-critical applications, showing that the sample complexity for adversarial learning is equivalent to nominal learning under certain assumptions, with validation on a damped pendulum example.
Motivated by bridging the simulation to reality gap in the context of safety-critical systems, we consider learning adversarially robust stability certificates for unknown nonlinear dynamical systems. In line with approaches from robust control, we consider additive and Lipschitz bounded adversaries that perturb the system dynamics. We show that under suitable assumptions of incremental stability on the underlying system, the statistical cost of learning an adversarial stability certificate is equivalent, up to constant factors, to that of learning a nominal stability certificate. Our results hinge on novel bounds for the Rademacher complexity of the resulting adversarial loss class, which may be of independent interest. To the best of our knowledge, this is the first characterization of sample-complexity bounds when performing adversarial learning over data generated by a dynamical system. We further provide a practical algorithm for approximating the adversarial training algorithm, and validate our findings on a damped pendulum example.