UCB Strategies in a Gaussian Two-Armed Bandit Problem

We consider the two-armed bandit problem in the application to batch data processing if there are two alternative processing methods with different a priori unknown efficiencies, and income is understood as successfully processed data. It is necessary to determine a more effective method and ensure its preferential use. Batch processing means that the incomes in batches have Gaussian distributions with a priori unknown one-step mathematical expectations and variances. This corresponds to a situation when the number of processed data batches and their volumes are of moderate size. We use UCB strategies for control. To calculate the regret, a recursive dynamic programming equation is obtained. Using the properties of UCB strategies, this equation was presented in a more computationally convenient form and then presented in an invariant form with a control horizon equal to one. The invariant equation does not depend on the total number of processed data, but only on the number of batches into which the data is divided and on the number of internal packets for which the variance is estimated.