ELMSO {ELMSO}

Main ELMSO Function

Description

This function allows you to allocate budget to a set of websites based on the cost curve of the websites and a matrix of pageviews for those sites.

Usage

ELMSO(z, CPM = NULL, a = NULL, tau = NULL, step = 0.05,
  size = 100, tol = 10^-3, iters = 200)

Arguments

z

An n by p matrix of pageviews

CPM

A p-dimensional vector of the average CPM values at each website. This is used to calculate the cost curve from a shifted logistic function. You may instead enter values for a p-dimensional "a" vector to define your own shifted logistic cost curve.

a

A p-dimensional vector of values controlling the steepness of the shifted logistic cost curve. You may instead enter values for a p-dimensional vector of average CPM values to have the curve calculated for you.

tau

A p-dimensional vector of total pageviews (in thousands) for each website. Defaults to the total pageviews in the matrix for each website (i.e., assumes z matrix represents all website pageviews) divided by 1000.

step

A value to control the step size of the lambda grid (distance between budget points). Default is 0.05.

size

A value to control the number of lambda values tried (number of budget points). Default is 100.

tol

A value to control the convergence tolerance of the coordinate descent procedure. Default is 10^-3.

iters

A value to control the number of iterations until algorithm should exit if convergence tolerance is not reached. Default is 200.

Value

bid: A matrix of bid values by website at each budget

spend: a matrix of total spend by website at each budget

budget: a vector of budget values

lambda: a vector of lambda values

a: a vector of a values (used to calculate shifted logistic curves and reach in reach.ELMSO function)

References

Courtney Paulson, Lan Luo, and Gareth M. James (2018) Efficient Large-Scale Internet Media Selection Optimization for Online Display Advertising. Journal of Marketing Research: August 2018, Vol. 55, No. 4, pp. 489-506.

Examples

z=matrix(round(abs(rnorm(5000,0,0.7))),1000,5)
CPM.avg=c(3,4,5,6,7)
tau.values=rep(1000,5) #Note tau here is in thousands of pageviews

allocation=ELMSO(z=z,CPM=CPM.avg,tau=tau.values)
allocation$bid
allocation$spend
allocation$budget
allocation$lambda
allocation$a