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We consider the online shortest path routing (SPR) of a network with stochastically time varying link states under potential adversarial attacks. Due to the denial of service (DoS) attacks, the distributions of link states could be stochastic (benign) or adversarial at different temporal and spatial locations. Without any a priori, designing an adaptive and optimal DoS-proof SPR protocol to thwart all possible adversarial attacks is a very challenging issue. In this paper, we present the first such integral solution based on the multi-armed bandit (MAB) theory, where jamming is the adversarial strategy. By introducing a novel control parameter into the exploration phase for each link, a martingale inequality is applied in our formulated combinatorial adversarial MAB framework. The proposed algorithm could automatically detect the specific jammed and un-jammed links within a unified framework. As a result, the adaptive online SPR strategies with near-optimal learning performance in all possible regimes are obtained. Moreover, we propose the accelerated algorithms by multi-path route probing and cooperative learning among multiple sources, and study their implementation issues. Comparing to existing works, our algorithm has the respective 30.3% and 87.1% improvements of network delay for oblivious jamming and adaptive jamming given a typical learning period and a 81.5% improvement of learning duration under a specified network delay on average, while it enjoys almost the same performance without jamming. Lastly, the accelerated algorithms can achieve a maximal of 150.2% improvement in network delay and a 431.3% improvement in learning duration.
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