  We obtain the upper bound of the loss function for a strategy in the
multi-armed bandit problem with Gaussian distributions of incomes. Considered
strategy is an asymptotic generalization of the strategy proposed by J. Bather
for the multi-armed bandit problem and using UCB rule, i.e. choosing the action
corresponding to the maximum of the upper bound of the confidence interval of
the current estimate of the expected value of one-step income. Results are
obtained with the help of invariant description of the control on the unit
horizon in the domain of close distributions because just there the loss
function attains its maximal values. UCB rule is widely used in machine
learning. It can be also used for the batch data processing optimization if
there are two alternative processing methods available with different a priori
unknown efficiencies.
