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We consider the minimax setup for the two-armed bandit problem as applied todata processing if there are two alternative processing methods available withdifferent a priori unknown efficiencies. One should determine the mosteffective method and provide its predominant application. To this end we usethe mirror descent algorithm (MDA). It is well-known that corresponding minimaxrisk has the order $N^{1/2}$ with $N$ being the number of processed data. Weimprove significantly the theoretical estimate of the factor using Monte-Carlosimulations. Then we propose a parallel version of the MDA which allowsprocessing of data by packets in a number of stages. The usage of parallelversion of the MDA ensures that total time of data processing depends mostly onthe number of packets but not on the total number of data. It is quiteunexpectedly that the parallel version behaves unlike the ordinary one even ifthe number of packets is large. Moreover, the parallel version considerablyimproves control performance because it provides significantly smaller value ofthe minimax risk. We explain this result by considering another parallelmodification of the MDA which behavior is close to behavior of the ordinaryversion. Our estimates are based on invariant descriptions of the algorithms.All estimates are obtained by Monte-Carlo simulations. It's worth noting thatparallel version performs well only for methods with close efficiencies. Ifefficiencies differ significantly then one should use the combined algorithmwhich at initial sufficiently short control horizon uses ordinary version andthen switches to the parallel version of the MDA.

Two-Armed Bandit Problem, Data Processing, and Parallel Version of the Mirror Descent Algorithm