Bayesian nonparametric bandits
type: Item
instance of: scholarly article
title: Bayesian nonparametric bandits
zbMATH Open document ID: 0587.62151
author: Murray K. Clayton
author: Donald A. Berry
published in: The Annals of Statistics
publication date: 1985-01-01T00:00:00Z
review text: A finite number (n) of selections are to be made from two independent stochastic processes, or ''arms''. The choice of arm at each stage is allowed to depend upon the full history of the process and the aim is to maximise the expectation of the sum of the observations. One arm produces i.i.d. observations with known probability measure, whereas observations from the other have a probability measure which is a Dirichlet process with parameter \(\alpha\). Call this latter process arm 1. Various monotonicity properties of optimal strategies are established, yielding corollaries of a ''stay-with-a-winner'' kind. For example, there exists a quantity \(b_ n(\alpha)\) such that if arm 1 is optimal initially and if \(X_ 1=x\) is observed then arm 1 is optimal again provided \(x\geq b_ n(\alpha).\) The determination of \(b_ n(\alpha)\) requires finding an optional strategy! However a simple upper bound is available which can be used to approximate an optimal rule. Calculations give some insight into the quality of such an approximation.
Mathematics Subject Classification ID: 62L05
Mathematics Subject Classification ID: 62L15
Mathematics Subject Classification ID: 62C10
Mathematics Subject Classification ID: 90C39
zbMATH DE Number: 3942836
zbMATH Keywords: sequential selections
zbMATH Keywords: sequential decisions
zbMATH Keywords: nonparametric decisions
zbMATH Keywords: one-armed bandits
zbMATH Keywords: two-armed bandits
zbMATH Keywords: Dirichlet process
zbMATH Keywords: monotonicity properties of optimal strategies
zbMATH Keywords: stay-with-a-winner
zbMATH Keywords: optional strategy
zbMATH Keywords: upper bound
zbMATH Keywords: approximation
reviewed by: Kevin D. Glazebrook
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176349753
OpenAlex ID: W2070725466
DOI: 10.1214/AOS/1176349753
description: scientific article; zbMATH DE number 3942836