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We address the adaptive stochastic control problem for a discrete time system described by controlled Markov chain with finite number of states. The mirror descent randomized control algorithm on the class of controlled homogeneous finite Markov chains with unknown mean losses has been proposed and studied. Here we develop the approach represented in Nazin and Miller (2011). The main assumptions are the following: processes are independent and stationary, nonnegative random losses are almostdoi:10.1109/cdc.2011.6161477 dblp:conf/cdc/NazinM11 fatcat:kqkidr2cxrfglhhr3tc6pisxim