Gaussian Two-Armed Bandit and Optimization of Batch Data Processing


Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

We consider the minimax setting for the two-armed bandit problem with normally distributed incomes having a priori unknown mathematical expectations and variances. This setting naturally arises in optimization of batch data processing where two alternative processing methods are available with different a priori unknown efficiencies. During the control process, it is required to determine the most efficient method and ensure its predominant application. We use the main theorem of game theory to search for minimax strategy and minimax risk as Bayesian ones corresponding to the worst-case prior distribution. To find them, a recursive integro-difference equation is obtained. We show that batch data processing almost does not increase the minimax risk if the number of batches is large enough.

About the authors

A. V. Kolnogorov

Department of Applied Mathematics and Information Science

Author for correspondence.
Email: kolnogorov53@mail.ru
Russian Federation, Moscow

Supplementary files

Supplementary Files
Action
1. JATS XML

Copyright (c) 2018 Pleiades Publishing, Inc.