Abstract
Abstract Adaptive control of discrete time Markov processes with an infinite time horizon risk sensitive cost functional is investigated. The transition probability for the Markov process depends on an unknown parameter. It is shown that the optimal risk sensitive cost is a continuous function of the parameter. Two almost optimal adaptive procedures that are based on the large deviations of the cost functional and discretized maximum likelihood estimates are described. A finite family of continuous control functions, where one control function is fixed after a nonrandom time that is explicitly given for each of the adaptive procedures, provides an almost optimal adaptive control.
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