Consider a decision maker who is responsible to dynamically collect observations so as to enhance his information in a speedy manner about an underlying phenomena of interest while accounting for the cost of data coll...
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ISBN:
(纸本)9781457705953
Consider a decision maker who is responsible to dynamically collect observations so as to enhance his information in a speedy manner about an underlying phenomena of interest while accounting for the cost of data collection. Due to the sequential nature of the problem, the decision maker relies on his current information state to adaptively (re-) evaluate the tradeoff between the cost of various sensing actions and the precision of their outcomes. In this paper, using results in dynamic programming, a lower bound for the optimal total cost is established. Moreover, an upper bound is obtained using a heuristic policy for dynamic selection of actions. Using the obtained bounds, the closed loop (feedback) gain is shown to be at least logarithmic in the penalty associated with wrong declarations. Furthermore, it is shown that the proposed heuristic achieves asymptotic optimality in many practically relevant problems such as variable-length coding with feedback and noisy dynamic search.
active sequential hypothesis testing (ASHT) is an extension of the classical sequentialhypothesistesting problem with controls. Chernoff [1] proposed a policy called Procedure A and showed its asymptotic optimality ...
详细信息
ISBN:
(纸本)9781479971954
active sequential hypothesis testing (ASHT) is an extension of the classical sequentialhypothesistesting problem with controls. Chernoff [1] proposed a policy called Procedure A and showed its asymptotic optimality as the cost of sampling was driven to zero. In this paper we study a further extension where we introduce costs for switching of actions. We show that a modification of Chernoff's Procedure A, one that we call Sluggish Procedure A, is asymptotically optimal even with switching costs. The growth rate of the total cost, as the probability of false detection is driven to zero, and as a switching parameter of the Sluggish Procedure A is driven down to zero, is the same as that without switching costs.
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