Optimization of two-alternative batch processing with parameter estimation based on data inside batches

We consider optimization of two-alternative batch data processing within the framework of the Gaussian one-armed bandit problem. This means that there are two alternative processing methods with different efficiencies and the effectiveness of the second method is a priori unknown. It is necessary to determine which method is more effective and ensure its preferential use, so that the effectiveness of the second method is evaluated during the data processing inside batches. This approach is advisable to use if the volumes of batches and their number are not very large. Recursive equations for calculating Bayesian risk and regret in the usual and invariant form with a control horizon equal to one are obtained.