UCB Strategy for Batch Data Processing on an Unknown Horizon

We consider the problem of a Gaussian two-armed bandit, which arises when optimizing batch processing of data. Suppose there are two processing methods with unknown efficiency. During the processing process, it is necessary to determine the best method and ensure its preferential use. The control goal is considered in a minimax setting, and UCB strategies are used to achieve it. With a large count of data, determining the optimal strategy takes a long time. To solve this problem, we suggest using regression analysis. Using regression analysis, we calculated how the maximum normalized regrets will change if the count of data varies in the range from 5 thousand to 100 thousand. We propose to use the obtained dependencies on an unknown control horizon. The article presents numerical results and shows the choice of a strategy based on the dependencies obtained. We used the Monte Carlo method to simulate control in a random environment.