Controlled Sensing for Sequential Multihypothesis Testing

The problem of multiple hypothesis testing with observation control is considered in the sequential setting.  In the case of uniform sensing cost, 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.  Then, a new model for controlled sensing for sequential multihypothesis testing is proposed.  This new model generalizes the existing model in two aspects.  First, it includes a more complicated memory structure in the controlled observations. Second, it allows for a general cost that can depend on the realizations of both the observations and control values.  Consequently, this new model is relevant to a wider class of applications, particularly in distributed and mobile sensor networks.  A sequential test is proposed for this new model and is shown to be asymptotically optimal.  Furthermore, the control policy associated with our asymptotically optimal test is shown be a self-tuning control policy that asymptotically achieves certain maximum rewards under all hypotheses simultaneously. (This is  joint work with Dr. George Atia and Professor Venugopal V. Veeravalli.)