  Applications in machine learning, optimization, and control require the
sequential selection of a few system elements, such as sensors, data, or
actuators, to optimize the system performance across multiple time steps.
However, in failure-prone and adversarial environments, sensors get attacked,
data get deleted, and actuators fail. Thence, traditional sequential design
paradigms become insufficient and, in contrast, resilient sequential designs
that adapt against system-wide attacks, deletions, or failures become
important. In general, resilient sequential design problems are computationally
hard. Also, even though they often involve objective functions that are
monotone and (possibly) submodular, no scalable approximation algorithms are
known for their solution. In this paper, we provide the first scalable
algorithm, that achieves the following characteristics: system-wide resiliency,
i.e., the algorithm is valid for any number of denial-of-service attacks,
deletions, or failures; adaptiveness, i.e., at each time step, the algorithm
selects system elements based on the history of inflicted attacks, deletions,
or failures; and provable approximation performance, i.e., the algorithm
guarantees for monotone objective functions a solution close to the optimal. We
quantify the algorithm's approximation performance using a notion of curvature
for monotone (not necessarily submodular) set functions. Finally, we support
our theoretical analyses with simulated experiments, by considering a
control-aware sensor scheduling scenario, namely, sensing-constrained robot
navigation.
