Near Optimal Adaptive Shortest Path Routing with Stochastic Links States under Adversarial Attack

We consider the shortest path routing (SPR) of a network with stochastically time varying link metrics under potential adversarial attacks. Due to potential denial of service attacks, the distributions of link states could be stochastic (benign) or adversarial at different temporal and spatial locations. Without any \emph{a priori}, designing an adaptive SPR protocol to cope with all possible situations in practice optimally is a very challenging issue. In this paper, we present the first solution by formulating it as a multi-armed bandit (MAB) problem. By introducing a novel control parameter into the exploration phase for each link, a martingale inequality is applied in the our combinatorial adversarial MAB framework. As such, our proposed algorithms could automatically detect features of the environment within a unified framework and find the optimal SPR strategies with almost optimal learning performance in all possible cases over time. Moreover, we study important issues related to the practical implementation, such as decoupling route selection with multi-path route probing, cooperative learning among multiple sources, the "cold-start" issue and delayed feedback of our algorithm. Nonetheless, the proposed SPR algorithms can be implemented with low complexity and they are proved to scale very well with the network size. Comparing to existing approaches in a typical network scenario under jamming attacks, our algorithm has a 65.3\% improvement of network delay given a learning period and a 81.5\% improvement of learning duration under a specified network delay.