This paper considers the problem of sequential binary hypothesis testing based on observations from a network of m sensors where a subset of the sensors is compromised by a malicious adversary. The asymptotic average sample number required to reach a certain level of error probability is selected as the performance metric of the system. We propose an asymptotically optimal voting algorithm for the sensor network with a fusion center and generalize it to fully-distributed networks, where the algorithm stays asymptotically optimal under the weak assumption that the sensor network is connected. Moreover, we prove that both of the proposed algorithms are asymptotically optimal in the presence of Byzantine sensors, in the sense that each of them forms a Nash equilibrium with the worst-case attack (flip-attack). Compared to existing distributed detection strategies, the proposed scheme has a low message complexity, which is independent of the error probability and the sample number, by taking advantage of the sparsity of votes. The results are corroborated by numerical simulations.

中文翻译：

---

使用拜占庭传感器进行分布式顺序假设检验


本文考虑了基于 m 个传感器网络的观察的顺序二元假设检验问题，其中传感器的子集受到恶意对手的破坏。选择达到一定误差概率水平所需的渐近平均样本数作为系统的性能指标。我们提出了一种针对具有融合中心的传感器网络的渐近最优投票算法，并将其推广到全分布式网络，其中该算法在传感器网络连接的弱假设下保持渐近最优。此外，我们证明所提出的两种算法在存在拜占庭传感器的情况下都是渐近最优的，因为它们中的每一个都与最坏情况的攻击（翻转攻击）形成纳什均衡。与现有的分布式检测策略相比，该方案利用投票的稀疏性，具有较低的消息复杂度，且与错误概率和样本数无关。结果通过数值模拟得到证实。