Resilient Monotone Sequential Maximization

Applications in machine learning, optimization, andcontrol require the sequential selection of a few system elements,such as sensors, data, or actuators, to optimize the systemperformance across multiple time steps. However, in failure-proneand adversarial environments, sensors get attacked, data getdeleted, and actuators fail. Thence, traditional sequential designparadigms become insufficient and, in contrast, resilient sequen-tial designs that adapt against system-wide attacks, deletions, orfailures become important. In general, resilient sequential designproblems are computationally hard. Also, even though they ofteninvolve objective functions that are monotone and (possibly)submodular, no scalable approximation algorithms are knownfor their solution. In this paper, we provide the first scalablealgorithm, that achieves the following characteristics: system-wideresiliency, i.e., the algorithm is valid for any number of denial-of-service attacks, deletions, or failures; adaptiveness, i.e., at eachtime step, the algorithm selects system elements based on thehistory of inflicted attacks, deletions, or failures; and provableapproximation performance, i.e., the algorithm guarantees formonotone objective functions a solution close to the optimal.We quantify the algorithm’s approximation performance using anotion of curvature for monotone (not necessarily submodular)set functions. Finally, we support our theoretical analyses withsimulated experiments, by considering a control-aware sensorscheduling scenario, namely, sensing-constrained robot navigation.