Robust and Adaptive Sequential Submodular Optimization

Abstract

IEEE Emerging applications of control, estimation, and machine learning pose resource constraints that limit which of the available sensors, actuators, or data can be simultaneously used. Therefore, researchers have proposed solutions within discrete optimization frameworks where the optimization is performed over finite sets. In this paper, we consider such problems but in adversarial environments, where in every step a number of the chosen elements in the optimization is removed due to failures/attacks. Specifically, we consider for the first time a sequential version of the problem that allows us to observe the failures and adapt, while the attacker also adapts to our response. We call the novel problem Robust Sequential submodular Maximization (RSM). Generally, the problem is computationally hard and no scalable algorithm is known for its solution. In this paper, we propose Robust and Adaptive Maximization (RAM), the first scalable algorithm. RAM adapts in every step to the history of failures. Also, it guarantees a near-optimal performance. Finally, we demonstrate RAM's near-optimality in simulations across various application scenarios, along with its robustness against several failure types, from worst-case to random.