Batch Version of Thompson Sampling in the One-Armed Bandit Problem

We consider the optimization of batch data processing if there are two processing methods with a priori known efficiency of the first method. Mathematically it is described as a Gaussian one-armed bandit problem. We consider the cases of known and a priori unknown variance of one-step income and use Thompson Sampling as the optimization strategy. We obtain invariant description of the control. Numerical experiments show high efficiency of the strategy. A redundancy manifests itself here in several aspects. First, the batch processing, if it allows parallel processing, is much faster than processing of data one by one. At the same time, it almost does not increase the minimax risk if the number of batches is large enough. Second, batch processing allows to use the same control strategy for a wide class of processes which one-step incomes obey the central limit theorem. Third, despite its simplicity, Thompson Sampling provides the high quality control, i.e., close to optimal minimax risk.