  We consider the problem of generating maximally adversarial disturbances for
a given controller assuming only blackbox access to it. We propose an online
learning approach to this problem that \emph{adaptively} generates disturbances
based on control inputs chosen by the controller. The goal of the disturbance
generator is to minimize \emph{regret} versus a benchmark
disturbance-generating policy class, i.e., to maximize the cost incurred by the
controller as well as possible compared to the best possible disturbance
generator \emph{in hindsight} (chosen from a benchmark policy class). In the
setting where the dynamics are linear and the costs are quadratic, we formulate
our problem as an online trust region (OTR) problem with memory and present a
new online learning algorithm (\emph{MOTR}) for this problem. We prove that
this method competes with the best disturbance generator in hindsight (chosen
from a rich class of benchmark policies that includes linear-dynamical
disturbance generating policies). We demonstrate our approach on two simulated
examples: (i) synthetically generated linear systems, and (ii) generating wind
disturbances for the popular PX4 controller in the AirSim simulator. On these
examples, we demonstrate that our approach outperforms several baseline
approaches, including $H_{\infty}$ disturbance generation and gradient-based
methods.
