One-armed bandit problem for parallel data processing systems

We consider the minimax setting for the one-armed bandit problem, i.e., for the two-armed bandit problem with a known distribution function of incomes corresponding to the first action. Incomes that correspond to the second action have normal distribution functions with unit variance and an unknown mathematical expectation. According to the main theorem of game theory, the minimax strategy and minimax risk are sought for as Bayesian, corresponding to the worst-case prior distribution. Results can be applied to parallel data processing systems if there are two processing methods available with an a priori known efficiency of the first.