Jacob Carruth, Maximilian F. Eggl, Charles L. Fefferman, Clarence W. Rowley, Melanie Weber
We consider a simple control problem in which the underlying dynamics depend on a parameter that is unknown and must be learned. We exhibit a control strategy which is optimal to within a multiplicative constant. While most authors find strategies which are successful as the time horizon tends to infinity, our strategy achieves lowest expected cost up to a constant factor for a fixed time horizon
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