Unified Framework for Numerical Optimizers.

optimizeR

The {optimizeR} package

• provides an object-oriented framework for optimizer functions in R
• and offers some convenience for useRs when minimizing or maximizing.

❌ You won’t need the package if you…

• already know which optimizer you want to use and if you are happy with its constraints (e.g., only minimization over the first function argument possible),
• want to compare optimizers that are already covered by {optimx} (Nash and Varadhan 2011) (they provide a framework to compare about 30 optimizers),
• or search for new optimization algorithms (because this package does not implement any optimizer functions itself).

✅ But you might find the package useful if you want to…

• compare any optimizer function (also those not covered by {optimx} or other frameworks; see the CRAN Task View: Optimization and Mathematical Programming (Schwendinger and Borchers 2023) for an overview of R optimizers),
• have consistently named inputs and outputs across different optimizers (which is generally not the case),
• view optimizers as objects (which can be helpful when implementing packages that depend on optimization),
• use optimizers for both minimization and maximization,
• optimize over more than one function argument,
• measure computation time or set a time limit for long optimization tasks.

How to use the package?

The following demo is a bit artificial but showcases the package purpose. Let’s assume we want to

• maximize a function over two of its arguments,
• interrupt optimization if it exceeds 10 seconds,
• and compare the performance between the optimizers 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

f <- function(a, b, x, y) {
  a * exp(-0.2 * sqrt(0.5 * (x^2 + y^2))) + exp(0.5 * (cos(2 * pi * x) + cos(2 * pi * y))) - exp(1) - b
}

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:

1. there are two target arguments (x and y) and
2. the position of the target argument is not in the first place.

Both 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 <- Objective$new(
  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:

nlm <- Optimizer$new(which = "stats::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…

nelder_mead <- Optimizer$new(which = "custom")
#> Please use method `$definition()` next to define a custom optimizer.

… and using the $definition() method next:

nelder_mead$definition(
  algorithm = 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:

nlm$seconds <- 10
nelder_mead$seconds <- 10

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

1. objective (either an objective object as defined above or just a function) and
2. initial (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.

nlm$maximize(objective = objective, initial = c(3, 3))
#> $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

nelder_mead$maximize(objective = objective, initial = c(3, 3))
#> $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.

How to get the access?

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.

Roadmap

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.

Getting in touch

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. 😊

References