We consider the minimax setup for the two-armed
bandit problem as applied to data processing if there are
two alternative processing methods available with different a
priori unknown efficiencies. One should determine the most
effective method and provide its predominant application. To
this end we use the mirror descent algorithm (MDA). It is
well-known that corresponding minimax risk has the order
N
1/2 with N being the number of processed data. We improve
significantly the theoretical estimate of the factor using MonteCarlo simulations. Then we propose a parallel version of the
MDA which allows processing of data by packets in a number
of stages. The usage of parallel version of the MDA ensures
that total time of data processing depends mostly on the
number of packets but not on the total number of data. It is
quite unexpectedly that the parallel version behaves unlike the
ordinary one even if the number of packets is large. Moreover,
the parallel version considerably improves control performance
because it provides significantly smaller value of the minimax
risk. We explain this result by considering another parallel
modification of the MDA which behavior is close to behavior
of the ordinary version. Our estimates are based on invariant
descriptions of the algorithms. All estimates are obtained by
Monte-Carlo simulations.
It’s worth noting that parallel version performs well only
for methods with close efficiencies. If efficiencies differ significantly then one should use the combined algorithm which at
initial sufficiently short control horizon uses ordinary version
and then switches to the parallel version of the MDA.