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We consider the shortest path routing (SPR) of a network with stochasticallytime varying link metrics under potential adversarial attacks. Due to potentialdenial of service attacks, the distributions of link states could be stochastic(benign) or adversarial at different temporal and spatial locations. Withoutany \emph{a priori}, designing an adaptive SPR protocol to cope with allpossible situations in practice optimally is a very challenging issue. In thispaper, we present the first solution by formulating it as a multi-armed bandit(MAB) problem. By introducing a novel control parameter into the explorationphase for each link, a martingale inequality is applied in the ourcombinatorial adversarial MAB framework. As such, our proposed algorithms couldautomatically detect features of the environment within a unified framework andfind the optimal SPR strategies with almost optimal learning performance in allpossible cases over time. Moreover, we study important issues related to thepractical implementation, such as decoupling route selection with multi-pathroute probing, cooperative learning among multiple sources, the "cold-start"issue and delayed feedback of our algorithm. Nonetheless, the proposed SPRalgorithms can be implemented with low complexity and they are proved to scalevery well with the network size. Comparing to existing approaches in a typicalnetwork scenario under jamming attacks, our algorithm has a 65.3\% improvementof network delay given a learning period and a 81.5\% improvement of learningduration under a specified network delay.

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