  We consider exponential two-armed bandit problem in which incomes are
described by exponential distribution densities. We develop Bayesian approach
and present recursive equation for determination of Bayesian strategy and
Bayesian risk. In the limiting case as the control horizon goes to infinity, we
obtain the second order partial differential equation in the domain of "close
distributions". Results are compared with Gaussian two-armed bandit. It turned
out that exponential and Gaussian two-armed bandits have the same description
in the limiting case. Since Gaussian two-armed bandit describes the batch
processing, this means that in case of exponential two-armed bandit batch
processing does not enlarge Bayesian risk in comparison with one-by-one optimal
processing as the total number of processed data items goes to infinity.
