noisyCE2-package {noisyCE2}

Cross-Entropy Optimisation of Noisy Functions

Description

The package noisyCE2 implements the cross-entropy algorithm (Rubinstein and Kroese, 2004) for the optimisation of unconstrained deterministic and noisy functions through a highly flexible and customisable function which allows user to define custom variable domains, sampling distributions, updating and smoothing rules, and stopping criteria. Several built-in methods and settings make the package very easy-to-use under standard optimisation problems.

Details

The package permits a noisy function to be maximised by means of the cross-entropy algorithm. Formally, problems in the form

\max_{x\in\Theta}\textbf{E}(f(x))

are tackled for a noisy function f\colon\Theta\subseteq\textbf{R}^m\to\textbf{R}.

Author(s)

Maintainer: Flavio Santi [e-mail] (ORCID)

References

Bee M., G. Espa, D. Giuliani, F. Santi (2017) "A cross-entropy approach to the estimation of generalised linear multilevel models", Journal of Computational and Graphical Statistics, 26 (3), pp. 695-708. https://doi.org/10.1080/10618600.2016.1278003

Rubinstein, R. Y., and Kroese, D. P. (2004), The Cross-Entropy Method, Springer, New York. ISBN: 978-1-4419-1940-3

See Also

Useful links:

• https://www.flaviosanti.it/software/noisyCE2

• Report bugs at https://github.com/f-santi/noisyCE2/issues

Examples

# EXAMPLE 1
# The negative 4-dimensional paraboloid can be maximised as follows:
negparaboloid <- function(x) { -sum((x - (1:4))^2) }
sol <- noisyCE2(negparaboloid, domain = rep('real', 4))

# EXAMPLE 2
# The 10-dimensional Rosenbrock's function can be minimised as follows:
rosenbrock <- function(x) {
  sum(100 * (tail(x, -1) - head(x, -1)^2)^2 + (head(x, -1) - 1)^2)
}

newvar <- type_real(
  init = c(0, 2),
  smooth = list(
    quote(smooth_lin(x, xt, 1)),
    quote(smooth_dec(x, xt, 0.7, 5))
  )
)

sol <- noisyCE2(
  rosenbrock, domain = rep(list(newvar), 10),
  maximise = FALSE, N = 2000, maxiter = 10000
)

# EXAMPLE 3
# The negative 4-dimensional paraboloid with additive Gaussian noise can be
# maximised as follows:
noisyparaboloid <- function(x) { -sum((x - (1:4))^2) + rnorm(1) }
sol <- noisyCE2(noisyparaboloid, domain = rep('real', 4), stoprule = geweke(x))
# where the stopping criterion based on the Geweke's test has been adopted
# according to Bee et al. (2017).