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The {optimizeR}
package
❌ You won’t need the package if you…
{optimx}
(Nash and Varadhan 2011) (they provide a framework to compare about 30
optimizers),✅ But you might find the package useful if you want to…
{optimx}
or other frameworks; see the CRAN Task View:
Optimization and Mathematical Programming (Schwendinger and Borchers
2023) for an overview of R optimizers),The following demo is a bit artificial but showcases the package purpose. Let’s assume we want to
stats::nlm
and pracma::nelder_mead
.We can easily do this task with {optimizeR}
:
library("optimizeR")
1. Define the objective function
Let \(f:\mathbb{R}^4\to\mathbb{R}\) with
<- function(a, b, x, y) {
f * exp(-0.2 * sqrt(0.5 * (x^2 + y^2))) + exp(0.5 * (cos(2 * pi * x) + cos(2 * pi * y))) - exp(1) - b
a }
For a = b = 20
, this is the inverted Ackley function
with a global maximum in x = y = 0
:
We want to keep a
and b
fixed here and
optimize over x
and y
(which are also both
single numeric values).
Two problems would occur if we would optimize f
with say
stats::nlm
directly:
x
and y
)
andBoth artifacts are not allowed by stats::nlm
and most of
other available optimizers, but supported by {optimizeR}
.
We just have to define an objective object which we later can pass to
the optimizers:
<- Objective$new(
objective f = f, # f is our objective function
target = c("x", "y"), # x and y are the target arguments
npar = c(1, 1), # the target arguments have both a length of 1
"a" = 20,
"b" = 20 # a and b have fixed values
)
2. Create the optimizer objects
Now that we have defined the objective function, let’s define our
optimizer objects. For stats::nlm
, this is a one-liner:
<- Optimizer$new(which = "stats::nlm") nlm
The {optimizeR}
package provides a dictionary of
optimizers, that can be directly selected via the which
argument. For an overview of available optimizers, see:
optimizer_dictionary#> <Dictionary> optimizer algorithms
#> Keys:
#> - lbfgsb3c::lbfgsb3c
#> - stats::nlm
#> - stats::nlminb
#> - stats::optim
#> - ucminf::ucminf
But in fact any optimizer that is not contained in the dictionary can
be put into the {optimizeR}
framework by setting
which = "custom"
first…
<- Optimizer$new(which = "custom")
nelder_mead #> Please use method `$definition()` next to define a custom optimizer.
… and using the $definition()
method next:
$definition(
nelder_meadalgorithm = pracma::nelder_mead, # the optimization function
arg_objective = "fn", # the argument name for the objective function
arg_initial = "x0", # the argument name for the initial values
out_value = "fmin", # the element for the optimal function value in the output
out_parameter = "xmin", # the element for the optimal parameters in the output
direction = "min" # the optimizer minimizes
)
3. Set a time limit
Each optimizer object has a field called $seconds
which
equals Inf
by default. You can optionally set a different,
single numeric value here to set a time limit in seconds for the
optimization:
$seconds <- 10
nlm$seconds <- 10 nelder_mead
Note that not everything (especially compiled C code) can technically
be timed out, see the help site
help("withTimeout", package = "R.utils")
for more
details.
4. Maximize the objective function
Each optimizer object has the two methods $maximize()
and $minimize()
for function maximization or minimization,
respectively. Both methods require values for the two arguments
objective
(either an objective object as defined above
or just a function) andinitial
(an initial parameter vector from where the
optimizer should start)and optionally accepts additional arguments to be passed to the optimizer or the objective function.
$maximize(objective = objective, initial = c(3, 3))
nlm#> $value
#> [1] -6.559645
#>
#> $parameter
#> [1] 1.974451 1.974451
#>
#> $seconds
#> [1] 0.01002908
#>
#> $initial
#> [1] 3 3
#>
#> $error
#> [1] FALSE
#>
#> $gradient
#> [1] 5.757896e-08 5.757896e-08
#>
#> $code
#> [1] 1
#>
#> $iterations
#> [1] 6
$maximize(objective = objective, initial = c(3, 3))
nelder_mead#> $value
#> [1] 0
#>
#> $parameter
#> [1] 0 0
#>
#> $seconds
#> [1] 0.005402327
#>
#> $initial
#> [1] 3 3
#>
#> $error
#> [1] FALSE
#>
#> $count
#> [1] 105
#>
#> $info
#> $info$solver
#> [1] "Nelder-Mead"
#>
#> $info$restarts
#> [1] 0
Note that
the inputs for the objective function and initial parameter values are named consistently across optimizers,
the output values for the optimal parameter vector and the maximimum function value are also named consistently across optimizers,
the output contains the initial parameter values and the optimization time in seconds and additionally other optimizer-specific elements,
pracma::nelder_mead
outperforms
stats::nlm
here both in terms of optimization time and
convergence to the global maximum.
You can install the released package version from CRAN with:
install.packages("optimizeR")
Then load the package via library("optimizeR")
and you
should be ready to go.
The following steps to further improve the package are currently on our agenda:
The package already provides a dictionary that stores optimizers
together with information about names of their inputs and outputs (see
the optimizer_dictionary
object). We want to extend this
dictionary with more optimizers that are commonly used.
We want to use alias for optimizers in the dictionary that group optimizers into classes (such as “unconstrained optimization”, “constrained Optimization”, “direct search”, “Newton-type” etc.). This would help to find alternative optimizers for a given task.
We want to implement a $summary()
method for an optimizer
object that gives an overview of the optimizer, its arguments, and its
properties.
You have a question, found a bug, request a feature, want to give feedback, or like to contribute? It would be great to hear from you, please file an issue on GitHub. 😊
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.