The problem of searching for $L$ anomalous processes among $M$ processes is considered. At each time, the decision maker can observe a subset of $K$ processes (i.e., multiple plays). The measurement drawn when observing a process follows one of two different distributions, depending on whether the process is normal or abnormal. The goal is to design a policy that minimizes the Bayes risk which balances between the sample complexity, detection errors, and the switching cost associated with switching across processes. We develop a policy, dubbed consecutive controlled sensing (CCS), to achieve this goal. On the one hand, by contrast to existing studies on controlled sensing, the CCS policy senses processes consecutively to reduce the switching cost. On the other hand, the policy controls the sensing operation in a closed-loop manner to switch between processes when necessary to guarantee reliable inference. We prove theoretically that CCS is asymptotically optimal in terms of minimizing the Bayes risk as the detection error approaches zero (i.e., the sample complexity increases). Simulation results demonstrate strong performance of CCS in the finite regime as well.
翻译:在以美元计的流程中寻找美元异常过程的问题得到了考虑。 决策者每次都可以观察到以美元计的流程子集( 多重剧本) 。 观察流程时的测量方法遵循两种不同的分布方法之一, 取决于该流程是否正常或异常。 目标是设计一种政策, 最大限度地减少贝雅斯风险, 平衡于抽样复杂性、 检测错误和与跨流程转换相关的转换成本。 我们为实现这一目标制定了一种政策, 称为连续连续控制遥感( CCS ) 。 一方面, 与现有的控制遥感研究相比, CCS 政策感知程序连续地降低转换成本。 另一方面, 政策以闭环方式控制感操作, 必要时在程序之间转换, 以保证可靠的推断。 我们从理论上证明, CCS 在最大限度地减少巴伊斯风险方面是最佳的, 与检测错误方法为零( 样本复杂性增加 ) 一样。 模拟结果显示, CCS 在有限的系统中也有很强的表现。