UCB strategies and optimization of batch processing in a one-armed bandit problem

We consider a Gaussian one-armed bandit problem, which arises when optimizing batch data processing if there are two alternative processing methods with a priori known efficiency of the first method. During processing, it is necessary to determine a more effective method and ensure its preferential use. This optimal control problem is interpreted as a game with nature. We investigate cases of known and a priori unknown variance of income corresponding to the second method. The control goal is considered in a minimax setting, and UCB strategies are used to ensure it. In all the studied cases, invariant descriptions of control on a horizon equal to one are obtained, which depend only on the number of batches into which the data is divided, but not on their full number. These descriptions allow us to determine approximately optimal parameters of strategies using Monte Carlo simulation. Numerical results show the high efficiency of the proposed UCB strategies.