Controlled sensing for sequential multihypothesis testing

The problem of controlled sensing for multihypothesis testing is considered. Prior to decision making, a controller sequentially chooses among a set of control actions to shape the quality of the observations. The goal is to design an efficient control policy, a stopping rule and a final decision rule, to minimize the expected stopping time subject to hard constraints on the risks associated with wrong decisions about each hypothesis. We propose a sequential test, which is shown to be asymptotically optimal when the risks are sufficiently small. Optimality is based on a derived lower bound on the minimum expected stopping time of tests in the class of tests satisfying the predefined risk constraints. Furthermore, by viewing the variable-length coding problem as a special case of sequential multihypothesis testing with observation control, we recover the classic result of Burnašev on the expected coding length for variable-length coding over Discrete Memoryless Channels (DMCs) at zero rate.