library(mlrMBO) library(rgenoud) set.seed(123) knitr::opts_chunk$set(cache = TRUE, collapse = FALSE) knitr::knit_hooks$set(document = function(x){ gsub("```\n*```r*\n*", "", x) })

The main goal of `mlrMBO`

is to optimize *expensive black-box functions* by *model-based optimization* (aka Bayesian optimization) and to provide a unified interface for different optimization tasks and algorithmic MBO variants.
Supported are, among other things:

- Efficient global optimization (EGO) of problems with numerical domain and Kriging as surrogate
- Using arbitrary regression models from mlr as surrogates
- Built-in parallelization using multi-point proposals
- Mixed-space optimization with categorical and subordinate parameters, for parameter configuration and tuning
- Multi-criteria optimization

This vignette gives a brief overview of the features of `mlrMBO`

.
A more detailed documentation can be found on: https://mlrmbo.mlr-org.com/.

Installing `mlrMBO`

will also install and load the dependencies `mlr`

, `ParamHelpers`

, and `smoof`

.
For this tutorial, you also need the additional packages `DiceKriging`

and `randomForest`

.

```
library(mlrMBO)
```

- Define
**objective function**and its parameters using the package`smoof`

. - Generate
**initial design**(optional). - Define
`mlr`

learner for**surrogate model**(optional). - Set up a
**MBO control**object. - Start the optimization with
`mbo()`

.

As a simple example we minimize a cosine-like function with an initial design of 5 points and 10 sequential MBO iterations. Thus, the optimizer is allowed 15 evaluations of the objective function in total to approximate the optimum.

Instead of manually defining the objective, we use the *smoof* package which offers many toy and benchmark functions for optimization.

obj.fun = makeCosineMixtureFunction(1) obj.fun = convertToMinimization(obj.fun) print(obj.fun) ggplot2::autoplot(obj.fun)

You are not limited to these test functions but can define arbitrary objective functions with *smoof*.

makeSingleObjectiveFunction( name = "my_sphere", fn = function(x) { sum(x*x) + 7 }, par.set = makeParamSet( makeNumericVectorParam("x", len = 2L, lower = -5, upper = 5) ), minimize = TRUE )

Check `?smoof::makeSingleObjectiveFunction`

for further details.

Before MBO can really start, it needs a set of already evaluated points - the *inital design*, as we have to initially learn our first machine learning regression model to propose new points for evaluation.
If no design is given (i.e. `design = NULL`

), `mbo()`

will use a *Maximin Latin Hypercube* `lhs::maximinLHS()`

design with `n = 4 * getNumberOfParameters(obj.fun)`

points.
If the design does not include function outcomes `mbo()`

will evaluate the design first before starting with the MBO algorithm.
In this example we generate our own design.

des = generateDesign(n = 5, par.set = getParamSet(obj.fun), fun = lhs::randomLHS)

We will also precalculate the results:

des$y = apply(des, 1, obj.fun)

*Note:* *mlrMBO* uses `y`

as a default name for the outcome of the objective function.
This can be changed in the control object.

We decide to use Kriging as our surrogate model because it has proven to be quite effective for numerical domains. The surrogate must be specified as a mlr regression learner:

surr.km = makeLearner("regr.km", predict.type = "se", covtype = "matern3_2", control = list(trace = FALSE))

*Note:* If no surrogate learner is defined, `mbo()`

automatically uses Kriging for a numerical domain, otherwise *random forest regression*.

The `MBOControl`

object allows customization of the optimization run and algorithmic behavior of MBO.
It is created with `makeMBOControl()`

, and can be modified with further setter-functions.

For further customization there are the following functions:

`setMBOControlTermination()`

: It is obligatory to define a termination criterion like the number of MBO iterations.`setMBOControlInfill()`

: It is recommended to set the infill criterion. For learners that support`predict.type = "se"`

the Confidence Bound`"cb"`

and the Expected Improvement`"ei"`

are a good choice.`setMBOControlMultiPoint()`

: Needed, in case you want to evaluate more then just one point per MBO-Iteration you can control this process here. This makes sense for parallelization.`setMBOControlMultiObj()`

: Needed, in case you want to optimize a multi-objective target function.

control = makeMBOControl() control = setMBOControlTermination(control, iters = 10) control = setMBOControlInfill(control, crit = makeMBOInfillCritEI())

Finally, we start the optimization process and print the result object. It contains the best best found solution and its corresponding objective value.

run = mbo(obj.fun, design = des, learner = surr.km, control = control, show.info = TRUE) print(run)

For more insights into the MBO process, we can also start the previous optimization with the function `exampleRun()`

instead of `mbo()`

.
This augments the results of `mbo()`

with additional information for plotting.
Here, we plot the optimization state at iterations 1, 2, and 10.

run = exampleRun(obj.fun, learner = surr.km, control = control, show.info = FALSE)

print(run) plotExampleRun(run, iters = c(1L, 2L, 10L), pause = FALSE)

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