Distributed Chernoff Test: Optimal Decision Systems Over Networks
Distributed Chernoff Test: Optimal Decision Systems Over Networks
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DOI：
10.1109/tit.2020.3046191
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发表时间：
2018-09
影响因子：
2.5
通讯作者：
A. Rangi;M. Franceschetti;S. Maranò
中科院分区：
文献类型：
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作者：
A. Rangi;M. Franceschetti;S. Maranò
我们研究了传感器网络的“主动”决策，其中传感器的连续探测动作是通过不断从过去的观察中学习来主动选择的。我们考虑两种网络设置：有中心协调和没有中心协调。在第一种情况下，网络节点之间通过一个中心实体进行交互，该中心实体起到融合中心的作用。在第二种情况下，网络节点以完全分布式的方式交互。在这两种情况下，我们提出了顺序和适应性假设检验，扩展了经典的Chernoff检验。我们将所提出的测试的性能与最优顺序测试进行比较。在存在融合中心的情况下，我们的测试实现了与Chernoff测试相同的渐近最优性，当单位时间的观察成本趋于零时，达到决策所需的预期成本加上做出错误决策的预期成本，从而使风险最小化。在达到决策所需的较长时间内，该测试也是渐近最优的。此外，就通信而言，该测试非常节省，并且每个网络节点的通道使用的预期数量趋向于一个很小的常数。在分布式设置中，我们的测试实现了Chernoff测试的相同的渐近最优性，在风险和决策时间的较高时刻方面达到乘法常数。此外，与文献中提出的最先进的方案相比，该测试在通信方面是吝啬的。对这些测试的分析还扩展到考虑消息量化和随机擦除信道上的通信。
We study “active” decision making over sensor networks where the sensors’ sequential probing actions are actively chosen by continuously learning from past observations. We consider two network settings: with and without central coordination. In the first case, the network nodes interact with each other through a central entity, which plays the role of a fusion center. In the second case, the network nodes interact in a fully distributed fashion. In both of these scenarios, we propose sequential and adaptive hypothesis tests extending the classic Chernoff test. We compare the performance of the proposed tests to the optimal sequential test. In the presence of a fusion center, our test achieves the same asymptotic optimality of the Chernoff test, minimizing the risk, expressed by the expected cost required to reach a decision plus the expected cost of making a wrong decision, when the observation cost per unit time tends to zero. The test is also asymptotically optimal in the higher moments of the time required to reach a decision. Additionally, the test is parsimonious in terms of communications, and the expected number of channel uses per network node tends to a small constant. In the distributed setup, our test achieves the same asymptotic optimality of Chernoff’s test, up to a multiplicative constant in terms of both risk and the higher moments of the decision time. Additionally, the test is parsimonious in terms of communications in comparison to state-of-the-art schemes proposed in the literature. The analysis of these tests is also extended to account for message quantization and communication over channels with random erasures.