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Due to the limit spectrum resource in the underwater acoustic networks, underwater cognitive acoustic communication is a promising technique. The channel sharing mechanism in cognitive networks can improve the communication capacity efficiently. Jamming attack is a common deny of service attack in cognitive networks. In the underwater cognitive acoustic networks, the anti-jamming problem is quite different from cognitive radio networks. It calls for an effective anti-jamming strategy in the cognitive acoustic channel access. In this article, we propose an online learning anti-jamming algorithm called multi-armed bandit–based acoustic channel access algorithm to achieve the jamming-resilient cognitive acoustic communication. The imperfect channel sensing and the constraints of underwater acoustic communication are considered in the anti-jamming game. Under different kinds of jamming attacks, the channel utilization can be improved with our jamming-resilient approach.