  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 adaptively generates disturbances based
on control inputs chosen by the controller. The goal of the disturbance
generator is to minimize 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 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
(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.
