Controlled Sensing for Multihypothesis Testing

    Authors

    S. Nitinawarat; G. K. Atia;V. V. Veeravalli

    Comments

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    Abbreviated Journal Title

    IEEE Trans. Autom. Control

    Keywords

    Chernoff information; controlled sensing; design of experiments; detection and estimation theory; error exponent; hypothesis testing; Markov decision process; PROBABILITY RATIO TESTS; DISCRIMINATION; Automation & Control Systems; Engineering, Electrical & Electronic

    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.

    Journal Title

    Ieee Transactions on Automatic Control

    Volume

    58

    Issue/Number

    10

    Publication Date

    1-1-2013

    Document Type

    Article

    Language

    English

    First Page

    2451

    Last Page

    2464

    WOS Identifier

    WOS:000324931000002

    ISSN

    0018-9286

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