| Title: | Implementation of the Efficient Large-Scale Online Display Advertising Algorithm |
|---|---|
| Description: | An implementation of the algorithm described in "Efficient Large- Scale Internet Media Selection Optimization for Online Display Advertising" by Paulson, Luo, and James (Journal of Marketing Research 2018; see URL below for journal text/citation and <http://faculty.marshall.usc.edu/gareth-james/Research/ELMSO.pdf> for a full-text version of the paper). The algorithm here is designed to allocate budget across a set of online advertising opportunities using a coordinate-descent approach, but it can be used in any resource-allocation problem with a matrix of visitation (in the case of the paper, website page- views) and channels (in the paper, websites). The package contains allocation functions both in the presence of bidding, when allocation is dependent on channel-specific cost curves, and when advertising costs are fixed at each channel. |
| Authors: | Courtney Paulson [aut, cre], Lan Luo [ctb], Gareth James [ctb] |
| Maintainer: | Courtney Paulson <[email protected]> |
| License: | GPL-3 |
| Version: | 1.0.1 |
| Built: | 2024-10-31 22:12:35 UTC |
| Source: | https://github.com/cran/ELMSO |
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.
ELMSO(z, CPM = NULL, a = NULL, tau = NULL, step = 0.05, size = 100, tol = 10^-3, iters = 200)ELMSO(z, CPM = NULL, a = NULL, tau = NULL, step = 0.05, size = 100, tol = 10^-3, iters = 200)
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. |
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)
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.
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$az=matrix(round(abs(rnorm(5000,0,0.7))),1000,5) CPM.avg=c(3,4,5,6,7) tau.values=rep(1000,5) #Note tau here is in thousands of pageviews allocation=ELMSO(z=z,CPM=CPM.avg,tau=tau.values) allocation$bid allocation$spend allocation$budget allocation$lambda allocation$a
This function allows you to allocate budget to a set of websites when cost is fixed at each website based on a matrix of pageviews for those sites.
ELMSO.fixed(z, CPM, tau = NULL, step = 0.05, size = 100, tol = 10^-3, iters = 200)ELMSO.fixed(z, CPM, tau = NULL, step = 0.05, size = 100, tol = 10^-3, iters = 200)
z |
An n by p matrix of pageviews |
CPM |
A p-dimensional vector of the (fixed) CPM values at each website |
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. |
spend: a matrix of total spend by website at each budget
budget: a vector of budget values
lambda: a vector of lambda values
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.
z=matrix(round(abs(rnorm(5000,0,0.7))),1000,5) CPM.fixed=c(3,4,5,6,7) tau.values=rep(100,5) #Note tau here is in thousands of pageviews allocation=ELMSO.fixed(z=z,CPM=CPM.fixed,tau=tau.values) allocation$spend allocation$budget allocation$lambdaz=matrix(round(abs(rnorm(5000,0,0.7))),1000,5) CPM.fixed=c(3,4,5,6,7) tau.values=rep(100,5) #Note tau here is in thousands of pageviews allocation=ELMSO.fixed(z=z,CPM=CPM.fixed,tau=tau.values) allocation$spend allocation$budget allocation$lambda
This function allows you to calculate reach achieved at a given budget value from the ELMSO output.
reach.ELMSO(bid, a, z)reach.ELMSO(bid, a, z)
bid |
A p-dimensional vector of the bidded CPM at each website for a particular budget value |
a |
A p-dimensional vector of steepness values for the cost curves associated with each website |
z |
An n by p matrix of pageviews |
A value between 0 and 1 specifying the reach achieved with the given budget allocation.
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.
z=matrix(round(abs(rnorm(5000,0,0.7))),1000,5) CPM.avg=c(3,4,5,6,7) tau.values=rep(100,5) #Note tau here is in thousands of pageviews allocation=ELMSO(z=z,CPM=CPM.avg,tau=tau.values) reach.ELMSO(allocation$bid[,101],allocation$a,z)z=matrix(round(abs(rnorm(5000,0,0.7))),1000,5) CPM.avg=c(3,4,5,6,7) tau.values=rep(100,5) #Note tau here is in thousands of pageviews allocation=ELMSO(z=z,CPM=CPM.avg,tau=tau.values) reach.ELMSO(allocation$bid[,101],allocation$a,z)
This function allows you to calculate reach achieved at a given budget value from the fixed ELMSO output.
reach.ELMSO.fixed(CPM, w, z, tau = NULL)reach.ELMSO.fixed(CPM, w, z, tau = NULL)
CPM |
A p-dimensional vector of the fixed CPM at each website for a particular budget value |
w |
A p-dimensional vector of amount spent at each website |
z |
An n by p matrix of pageviews |
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. |
A value between 0 and 1 specifying the reach achieved with the given budget allocation.
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.
z=matrix(round(abs(rnorm(5000,0,0.7))),1000,5) CPM.fixed=c(3,4,5,6,7) tau.values=rep(100,5) #Note tau here is in thousands of pageviews allocation=ELMSO.fixed(z=z,CPM=CPM.fixed,tau=tau.values) reach.ELMSO.fixed(CPM.fixed,allocation$spend[,101],z,tau.values)z=matrix(round(abs(rnorm(5000,0,0.7))),1000,5) CPM.fixed=c(3,4,5,6,7) tau.values=rep(100,5) #Note tau here is in thousands of pageviews allocation=ELMSO.fixed(z=z,CPM=CPM.fixed,tau=tau.values) reach.ELMSO.fixed(CPM.fixed,allocation$spend[,101],z,tau.values)