Controlled sensing for multihypothesis testing

Sirin Nitinawarat, George K. Atia, Venugopal V. Veeravalli

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number6513292
Pages (from-to)2451-2464
Number of pages14
JournalIEEE Transactions on Automatic Control
Issue number10
StatePublished - 2013


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

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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