Title

Controlled Sensing For Multihypothesis Testing

Keywords

Chernoff information; controlled sensing; design of experiments; detection and estimation theory; error exponent; hypothesis testing; Markov decision process

Abstract

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. © 2013 IEEE.

Publication Date

10-4-2013

Publication Title

IEEE Transactions on Automatic Control

Volume

58

Issue

10

Number of Pages

2451-2464

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1109/TAC.2013.2261188

Socpus ID

84884515307 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84884515307

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