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首页> 外文期刊>IEEE Transactions on Automatic Control >Controlled Sensing for Multihypothesis Testing
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Controlled Sensing for Multihypothesis Testing

机译：多假设测试的控制感测

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摘要

The problem of multiple hypothesis testing with observation control is considered in both fixed sample size and sequential settings. In the fixed sample size setting, for binary hypothesis testing, the optimal exponent for the maximal error probability corresponds to the maximum Chernoff information over the choice of controls, and a pure stationary open-loop control policy is asymptotically optimal within the larger class of all causal control policies. For multihypothesis testing in the fixed sample size setting, lower and upper bounds on the optimal error exponent are derived. It is also shown through an example with three hypotheses that the optimal causal control policy can be strictly better than the optimal open-loop control policy. In the sequential setting, a test based on earlier work by Chernoff for binary hypothesis testing, is shown to be first-order asymptotically optimal for multihypothesis testing in a strong sense, using the notion of decision making risk in place of the overall probability of error. Another test is also designed to meet hard risk constrains while retaining asymptotic optimality. The role of past information and randomization in designing optimal control policies is discussed.
机译：<？Pub Dtl？>在固定样本量和顺序设置中都考虑了带有观察控制的多重假设检验问题。在固定样本量设置中，对于二元假设检验，最大误差概率的最佳指数对应于控制选择上的最大切尔诺夫信息，并且在所有类别的较大类别中，纯静态开环控制策略是渐近最优的因果控制政策。对于在固定样本大小设置下的多假设检验，得出最佳误差指数的上下限。通过带有三个假设的示例也表明，最佳因果控制策略可以比最佳开环控制策略严格更好。在顺序设置中，基于切尔诺夫早期工作的二元假设检验的测试在强意义上被证明是一阶渐近最优的多假设检验，使用决策风险的概念代替了总错误概率。还设计了另一种测试，以在保持渐近最优性的同时满足严格的风险约束。讨论了过去的信息和随机化在设计最佳控制策略中的作用。

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