Computational Mathematics

A limiting description of control in a gaussian one-armed bandit problem

A. V. Kolnogorov

Yaroslav-the-Wise Novgorod State University, Veliky Novgorod, Russian Federation

Abstract: We consider a limiting description of control in a Gaussian one-armed bandit problem in application to batch processing of big data, if estimates of unknown mathematical expectation and variance of one-step incomes are performed during data processing within batches. This description is given by a second-order partial differential equation in which the estimate of the unknown variance is present as a constant parameter. This result means that when processing big data, an arbitrarily accurate estimate of the unknown variance can be obtained at a relatively arbitrarily short initial stage, and then used for control.

Keywords: Gaussian one-armed bandit, batch processing, Bayesian approach, invariant description.

UDC: 519.244, 519.83

MSC: 62C10, 62L05, 91A35

Received: 10.01.2025

Language: English

DOI: 10.14529/jcem250102