https://github.com/cran/GPGame
Tip revision: cbe720dc365499488a36511cbc106efe2acb5004 authored by Victor Picheny on 23 January 2022, 15:22:45 UTC
version 1.2.0
version 1.2.0
Tip revision: cbe720d
GPGame.Rd
% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/GPGame-package.R
\name{GPGame}
\alias{GPGame}
\title{Package GPGame}
\description{
Sequential strategies for finding game equilibria in a black-box setting (expensive pay-off evaluations, no derivatives).
Handles noiseless or noisy evaluations. Two acquisition functions are available. Graphical outputs can be generated automatically.
}
\details{
Important functions: \cr
\code{\link[GPGame]{solve_game}} \cr
\code{\link[GPGame]{plotGame}} \cr
}
\examples{
\donttest{
# To use parallel computation (turn off on Windows)
library(parallel)
parallel <- FALSE # TRUE #
if(parallel) ncores <- detectCores() else ncores <- 1
##############################################
# 2 variables, 2 players, Nash equilibrium
# Player 1 (P1) wants to minimize fun1 and player 2 (P2) fun2
# P1 chooses x2 and P2 x2
##############################################
# First, define objective function fun: (x1,x2) -> (fun1,fun2)
fun <- function (x)
{
if (is.null(dim(x))) x <- matrix(x, nrow = 1)
b1 <- 15 * x[, 1] - 5
b2 <- 15 * x[, 2]
return(cbind((b2 - 5.1*(b1/(2*pi))^2 + 5/pi*b1 - 6)^2 + 10*((1 - 1/(8*pi)) * cos(b1) + 1),
-sqrt((10.5 - b1)*(b1 + 5.5)*(b2 + 0.5)) - 1/30*(b2 - 5.1*(b1/(2*pi))^2 - 6)^2-
1/3 * ((1 - 1/(8 * pi)) * cos(b1) + 1)))
}
##############################################
# x.to.obj indicates that P1 chooses x1 and P2 chooses x2
x.to.obj <- c(1,2)
##############################################
# Define a discretization of the problem: each player can choose between 21 strategies
# The ensemble of combined strategies is a 21x21 cartesian grid
# n.s is the number of strategies (vector)
n.s <- rep(21, 2)
# gridtype is the type of discretization
gridtype <- 'cartesian'
integcontrol <- list(n.s=n.s, gridtype=gridtype)
##############################################
# Run solver with 6 initial points, 14 iterations
n.init <- 6 # number of initial points (space-filling)
n.ite <- 14 # number of iterations (sequential infill points)
res <- solve_game(fun, equilibrium = "NE", crit = "sur", n.init=n.init, n.ite=n.ite,
d = 2, nobj=2, x.to.obj = x.to.obj, integcontrol=integcontrol,
ncores = ncores, trace=1, seed=1)
##############################################
# Get estimated equilibrium and corresponding pay-off
NE <- res$Eq.design
Poff <- res$Eq.poff
##############################################
# Draw results
plotGame(res)
##############################################
# See solve_game for other examples
##############################################
}
}
\references{
V. Picheny, M. Binois, A. Habbal (2016+), A Bayesian Optimization approach to find Nash equilibria,
\emph{https://arxiv.org/abs/1611.02440}.
M. Binois, V. Picheny, A. Habbal, "The Kalai-Smorodinski solution for many-objective Bayesian optimization",
NIPS BayesOpt workshop, December 2017, Long Beach, USA,
\emph{https://bayesopt.github.io/papers/2017/28.pdf}.
}
\seealso{
\code{\link[DiceKriging]{DiceKriging-package}}, \code{\link[DiceOptim]{DiceOptim-package}}, \code{\link[KrigInv]{KrigInv-package}}, \code{\link[GPareto]{GPareto-package}}
}
\author{
Victor Picheny, Mickael Binois
}