`OptimizerMbo`

class that implements Model Based Optimization (MBO).
The implementation follows a modular layout relying on a loop_function determining the MBO flavor to be used, e.g.,
bayesopt_ego for sequential single-objective Bayesian Optimization, a Surrogate, an AcqFunction, e.g., mlr_acqfunctions_ei for
Expected Improvement and an AcqOptimizer.

MBO algorithms are iterative optimization algorithms that make use of a continuously updated surrogate model built for the objective function. By optimizing a comparably cheap to evaluate acquisition function defined on the surrogate prediction, the next candidate is chosen for evaluation.

Detailed descriptions of different MBO flavors are provided in the documentation of the respective loop_function.

Termination is handled via a bbotk::Terminator part of the bbotk::OptimInstance to be optimized.

Note that in general the Surrogate is updated one final time on all available data after the optimization process has terminated.
However, in certain scenarios this is not always possible or meaningful, e.g., when using `bayesopt_parego()`

for multi-objective optimization
which uses a surrogate that relies on a scalarization of the objectives.
It is therefore recommended to manually inspect the Surrogate after optimization if it is to be used, e.g., for visualization purposes to make
sure that it has been properly updated on all available data.
If this final update of the Surrogate could not be performed successfully, a warning will be logged.

## Archive

The bbotk::Archive holds the following additional columns that are specific to MBO algorithms:

`[acq_function$id]`

(`numeric(1)`

)

The value of the acquisition function.`.already_evaluated`

(`logical(1))`

Whether this point was already evaluated. Depends on the`skip_already_evaluated`

parameter of the AcqOptimizer.

## Super class

`bbotk::Optimizer`

-> `OptimizerMbo`

## Active bindings

`loop_function`

(loop_function |

`NULL`

)

Loop function determining the MBO flavor.`surrogate`

(Surrogate |

`NULL`

)

The surrogate.`acq_function`

(AcqFunction |

`NULL`

)

The acquisition function.`acq_optimizer`

(AcqOptimizer |

`NULL`

)

The acquisition function optimizer.`args`

(named

`list()`

)

Further arguments passed to the`loop_function`

. For example,`random_interleave_iter`

.`result_assigner`

(ResultAssigner |

`NULL`

)

The result assigner.`param_classes`

(

`character()`

)

Supported parameter classes that the optimizer can optimize. Determined based on the`surrogate`

and the`acq_optimizer`

. This corresponds to the values given by a paradox::ParamSet's`$class`

field.`properties`

(

`character()`

)

Set of properties of the optimizer. Must be a subset of`bbotk_reflections$optimizer_properties`

. MBO in principle is very flexible and by default we assume that the optimizer has all properties. When fully initialized, properties are determined based on the`loop_function`

and`surrogate`

.`packages`

(

`character()`

)

Set of required packages. A warning is signaled prior to optimization if at least one of the packages is not installed, but loaded (not attached) later on-demand via`requireNamespace()`

. Required packages are determined based on the`acq_function`

,`surrogate`

and the`acq_optimizer`

.

## Methods

## Inherited methods

### Method `new()`

Creates a new instance of this R6 class.

If `surrogate`

is `NULL`

and the `acq_function$surrogate`

field is populated, this Surrogate is used.
Otherwise, `default_surrogate(instance)`

is used.
If `acq_function`

is NULL and the `acq_optimizer$acq_function`

field is populated, this AcqFunction is used (and therefore its `$surrogate`

if populated; see above).
Otherwise `default_acqfunction(instance)`

is used.
If `acq_optimizer`

is NULL, `default_acqoptimizer(instance)`

is used.

Even if already initialized, the `surrogate$archive`

field will always be overwritten by the bbotk::Archive of the current bbotk::OptimInstance to be optimized.

For more information on default values for `loop_function`

, `surrogate`

, `acq_function`

and `acq_optimizer`

, see `?mbo_defaults`

.

#### Usage

```
OptimizerMbo$new(
loop_function = NULL,
surrogate = NULL,
acq_function = NULL,
acq_optimizer = NULL,
args = NULL,
result_assigner = NULL
)
```

#### Arguments

`loop_function`

(loop_function |

`NULL`

)

Loop function determining the MBO flavor.`surrogate`

(Surrogate |

`NULL`

)

The surrogate.`acq_function`

(AcqFunction |

`NULL`

)

The acquisition function.`acq_optimizer`

(AcqOptimizer |

`NULL`

)

The acquisition function optimizer.`args`

(named

`list()`

)

Further arguments passed to the`loop_function`

. For example,`random_interleave_iter`

.`result_assigner`

(ResultAssigner |

`NULL`

)

The result assigner.

### Method `reset()`

Reset the optimizer.
Sets the following fields to `NULL`

:
`loop_function`

, `surrogate`

, `acq_function`

, `acq_optimizer`

, `args`

, `result_assigner`

## Examples

```
# \donttest{
if (requireNamespace("mlr3learners") &
requireNamespace("DiceKriging") &
requireNamespace("rgenoud")) {
library(bbotk)
library(paradox)
library(mlr3learners)
# single-objective EGO
fun = function(xs) {
list(y = xs$x ^ 2)
}
domain = ps(x = p_dbl(lower = -10, upper = 10))
codomain = ps(y = p_dbl(tags = "minimize"))
objective = ObjectiveRFun$new(fun = fun, domain = domain, codomain = codomain)
instance = OptimInstanceSingleCrit$new(
objective = objective,
terminator = trm("evals", n_evals = 5))
surrogate = default_surrogate(instance)
acq_function = acqf("ei")
acq_optimizer = acqo(
optimizer = opt("random_search", batch_size = 100),
terminator = trm("evals", n_evals = 100))
optimizer = opt("mbo",
loop_function = bayesopt_ego,
surrogate = surrogate,
acq_function = acq_function,
acq_optimizer = acq_optimizer)
optimizer$optimize(instance)
# multi-objective ParEGO
fun = function(xs) {
list(y1 = xs$x^2, y2 = (xs$x - 2) ^ 2)
}
domain = ps(x = p_dbl(lower = -10, upper = 10))
codomain = ps(y1 = p_dbl(tags = "minimize"), y2 = p_dbl(tags = "minimize"))
objective = ObjectiveRFun$new(fun = fun, domain = domain, codomain = codomain)
instance = OptimInstanceMultiCrit$new(
objective = objective,
terminator = trm("evals", n_evals = 5))
optimizer = opt("mbo",
loop_function = bayesopt_parego,
surrogate = surrogate,
acq_function = acq_function,
acq_optimizer = acq_optimizer)
optimizer$optimize(instance)
}
#> WARN [16:09:16.222] [bbotk] Task 'surrogate_task' has missing values in column(s) 'y_scal', but learner 'regr.km' does not support this
#> WARN [16:09:16.222] [bbotk] Could not update the surrogate a final time after the optimization process has terminated.
#> x x_domain y1 y2
#> <num> <list> <num> <num>
#> 1: 1.816490 <list[1]> 3.299635 0.03367603
#> 2: 1.364403 <list[1]> 1.861596 0.40398355
# }
```