# Batch Data Processing and Gaussian Two-Armed Bandit

## TL;DR

This paper analyzes the Gaussian two-armed bandit problem in batch data processing, showing that large packet sizes can be used without significant loss in control performance, especially when processing methods have similar efficiencies.

## Contribution

It introduces a model for batch processing in the two-armed bandit framework and quantifies the impact of packet size and method efficiency differences on control risk.

## Key findings

- Large packet processing does not significantly increase minimax risk when methods are similarly efficient.
- Initial small-sized packets can mitigate losses when method efficiencies differ.
- Control performance remains robust with sufficiently large packet numbers.

## Abstract

We consider the two-armed bandit problem as applied to data processing if there are two alternative processing methods available with different a priori unknown efficiencies. One should determine the most effective method and provide its predominant application. Gaussian two-armed bandit describes the batch, and possibly parallel, processing when the same methods are applied to sufficiently large packets of data and accumulated incomes are used for the control. If the number of packets is large enough then such control does not deteriorate the control performance, i.e. does not increase the minimax risk. For example, in case of 50 packets the minimax risk is about 2% larger than that one corresponding to one-by-one optimal processing. However, this is completely true only for methods with close efficiencies because otherwise there may be significant expected losses at the initial stage of control when both actions are applied turn-by-turn. To avoid significant losses at the initial stage of control one should take initial packets of data having smaller sizes.