5.4 Parameters (using paradox
)
The paradox package offers a language for the description of parameter spaces, as well as tools for useful operations on these parameter spaces. A parameter space is often useful when describing:
- A set of sensible input values for an R function
- The set of possible values that slots of a configuration object can take
- The search space of an optimization process
The tools provided by paradox
therefore relate to:
- Parameter checking: Verifying that a set of parameters satisfies the conditions of a parameter space
- Parameter sampling: Generating parameter values that lie in the parameter space for systematic exploration of program behavior depending on these parameters
paradox is, by nature, an auxiliary package that derives its usefulness from other packages that make use of it. It is heavily utilized in other mlr-org packages such as mlr3, mlr3pipelines, and mlr3tuning.
5.4.1 Reference Based Objects
paradox is the spiritual successor to the ParamHelpers package and was written from scratch using the R6 class system.
The most important consequence of this is that all objects created in paradox
are “reference-based”, unlike most other objects in R.
When a change is made to a ParamSet
object, for example by adding a parameter using the $add()
function, all variables that point to this ParamSet
will contain the changed object.
To create an independent copy of a ParamSet
, the $clone()
method needs to be used:
library("paradox")
ps = ParamSet$new()
ps2 = ps
ps3 = ps$clone(deep = TRUE)
print(ps) # the same for ps2 and ps3
## ParamSet:
## Empty.
print(ps) # ps was changed
## ParamSet:
## id class lower upper levels default value
## 1: a ParamLgl NA NA TRUE,FALSE <NoDefault>
print(ps2) # contains the same reference as ps
## ParamSet:
## id class lower upper levels default value
## 1: a ParamLgl NA NA TRUE,FALSE <NoDefault>
print(ps3) # is a "clone" of the old (empty) ps
## ParamSet:
## Empty.
5.4.2 Defining a Parameter Space
5.4.2.1 Single Parameters
The basic building block for describing parameter spaces is the Param
class.
It represents a single parameter, which usually can take a single atomic value.
Consider, for example, trying to configure the rpart
package’s rpart.control
object.
It has various components (minsplit
, cp
, …) that all take a single value, and that would all be represented by a different instance of a Param
object.
The Param
class has various sub-classes that represent different value types:
ParamInt
: Integer numbersParamDbl
: Real numbersParamFct
: String values from a set of possible values, similar to Rfactor
sParamLgl
: Truth values (TRUE
/FALSE
), aslogical
s in RParamUty
: Parameter that can take any value
A particular instance of a parameter is created by calling the attached $new()
function:
library("paradox")
parA = ParamLgl$new(id = "A")
parB = ParamInt$new(id = "B", lower = 0, upper = 10, tags = c("tag1", "tag2"))
parC = ParamDbl$new(id = "C", lower = 0, upper = 4, special_vals = list(NULL))
parD = ParamFct$new(id = "D", levels = c("x", "y", "z"), default = "y")
parE = ParamUty$new(id = "E", custom_check = function(x) checkmate::checkFunction(x))
Every parameter must have:
- id - A name for the parameter within the parameter set
- default - A default value
- special_vals - A list of values that are accepted even if they do not conform to the type
- tags - Tags that can be used to organize parameters
The numeric (Int
and Dbl
) parameters furthermore allow for specification of a lower and upper bound.
Meanwhile, the Fct
parameter must be given a vector of levels that define the possible states its parameter can take.
The Uty
parameter can also have a custom_check
function that must return TRUE
when a value is acceptable and may return a character(1)
error description otherwise.
The example above defines parE
as a parameter that only accepts functions.
All values which are given to the constructor are then accessible from the object for inspection using $
.
Although all these values can be changed for a parameter after construction, this can be a bad idea and should be avoided when possible.
Instead, a new parameter should be constructed.
Besides the possible values that can be given to a constructor, there are also the $class
, $nlevels
, $is_bounded
, $has_default
, $storage_type
, $is_number
and $is_categ
slots that give information about a parameter.
A list of all slots can be found in ?Param
.
It is also possible to get all information of a Param
as data.table
by calling as.data.table
.
as.data.table(parA)
## id class lower upper levels nlevels is_bounded special_vals default storage_type tags
## 1: A ParamLgl NA NA TRUE,FALSE 2 TRUE <list> <NoDefault> logical
5.4.2.1.1 Type / Range Checking
A Param
object offers the possibility to check whether a value satisfies its condition, i.e. is of the right type, and also falls within the range of allowed values, using the $test()
, $check()
, and $assert()
functions.
test()
should be used within conditional checks and returns TRUE
or FALSE
, while check()
returns an error description when a value does not conform to the parameter (and thus plays well with the checkmate::assert()
function).
assert()
will throw an error whenever a value does not fit.
parA$test(FALSE)
## [1] TRUE
parA$test("FALSE")
## [1] FALSE
parA$check("FALSE")
## [1] "Must be of type 'logical flag', not 'character'"
Instead of testing single parameters, it is often more convenient to check a whole set of parameters using a ParamSet
.
5.4.2.2 Parameter Sets
The ordered collection of parameters is handled in a ParamSet
1.
It is initialized using the $new()
function and optionally takes a list of Param
s as argument.
Parameters can also be added to the constructed ParamSet
using the $add()
function.
It is even possible to add whole ParamSet
s to other ParamSet
s.
ps = ParamSet$new(list(parA, parB))
ps$add(parC)
ps$add(ParamSet$new(list(parD, parE)))
print(ps)
## ParamSet:
## id class lower upper levels default value
## 1: A ParamLgl NA NA TRUE,FALSE <NoDefault>
## 2: B ParamInt 0 10 <NoDefault>
## 3: C ParamDbl 0 4 <NoDefault>
## 4: D ParamFct NA NA x,y,z y
## 5: E ParamUty NA NA <NoDefault>
The individual parameters can be accessed through the $params
slot.
It is also possible to get information about all parameters in a vectorized fashion using mostly the same slots as for individual Param
s (i.e. $class
, $levels
etc.), see ?ParamSet
for details.
It is possible to reduce ParamSet
s using the $subset
method.
Be aware that it modifies a ParamSet in-place, so a “clone” must be created first if the original ParamSet
should not be modified.
psSmall = ps$clone()
psSmall$subset(c("A", "B", "C"))
print(psSmall)
## ParamSet:
## id class lower upper levels default value
## 1: A ParamLgl NA NA TRUE,FALSE <NoDefault>
## 2: B ParamInt 0 10 <NoDefault>
## 3: C ParamDbl 0 4 <NoDefault>
Just as for Param
s, and much more useful, it is possible to get the ParamSet
as a data.table
using as.data.table()
.
This makes it easy to subset parameters on certain conditions and aggregate information about them, using the variety of methods provided by data.table
.
as.data.table(ps)
## id class lower upper levels nlevels is_bounded special_vals default storage_type tags
## 1: A ParamLgl NA NA TRUE,FALSE 2 TRUE <list> <NoDefault> logical
## 2: B ParamInt 0 10 11 TRUE <list> <NoDefault> integer tag1,tag2
## 3: C ParamDbl 0 4 Inf TRUE <list> <NoDefault> numeric
## 4: D ParamFct NA NA x,y,z 3 TRUE <list> y character
## 5: E ParamUty NA NA Inf FALSE <list> <NoDefault> list
5.4.2.2.1 Type / Range Checking
Similar to individual Param
s, the ParamSet
provides $test()
, $check()
and $assert()
functions that allow for type and range checking of parameters.
Their argument must be a named list with values that are checked against the respective parameters.
It is possible to check only a subset of parameters.
5.4.2.2.2 Values in a ParamSet
Although a ParamSet
fundamentally represents a value space, it also has a slot $values
that can contain a point within that space.
This is useful because many things that define a parameter space need similar operations (like parameter checking) that can be simplified.
The $values
slot contains a named list that is always checked against parameter constraints.
When trying to set parameter values, e.g. for mlr3
Learner
s, it is the $values
slot of its $param_set
that needs to be used.
ps$values = list(A = TRUE, B = 0)
ps$values$B = 1
print(ps$values)
## $A
## [1] TRUE
##
## $B
## [1] 1
The parameter constraints are automatically checked:
5.4.2.2.3 Dependencies
It is often the case that certain parameters are irrelevant or should not be given depending on values of other parameters.
An example would be a parameter that switches a certain algorithm feature (for example regularization) on or off, combined with another parameter that controls the behavior of that feature (e.g. a regularization parameter).
The second parameter would be said to depend on the first parameter having the value TRUE
.
A dependency can be added using the $add_dep
method, which takes both the ids of the “depender” and “dependee” parameters as well as a Condition
object.
The Condition
object represents the check to be performed on the “dependee”.
Currently it can be created using CondEqual$new()
and CondAnyOf$new()
.
Multiple dependencies can be added, and parameters that depend on others can again be depended on, as long as no cyclic dependencies are introduced.
The consequence of dependencies are twofold:
For one, the $check()
, $test()
and $assert()
tests will not accept the presence of a parameter if its dependency is not met.
Furthermore, when sampling or creating grid designs from a ParamSet
, the dependencies will be respected (see Parameter Sampling, in particular Hierarchical Sampler).
The following example makes parameter D
depend on parameter A
being FALSE
, and parameter B
depend on parameter D
being one of "x"
or "y"
.
This introduces an implicit dependency of B
on A
being FALSE
as well, because D
does not take any value if A
is TRUE
.
ps$check(list(A = FALSE, D = "x", B = 1)) # OK: all dependencies met
## [1] TRUE
ps$check(list(A = FALSE, D = "z", B = 1)) # B's dependency is not met
## [1] "Condition for 'B' not ok: D anyof x, y; instead: D=z"
ps$check(list(A = FALSE, B = 1)) # B's dependency is not met
## [1] "Condition for 'B' not ok: D anyof x, y; instead: D=<not-there>"
ps$check(list(A = FALSE, D = "z")) # OK: B is absent
## [1] TRUE
ps$check(list(A = TRUE)) # OK: neither B nor D present
## [1] TRUE
ps$check(list(A = TRUE, D = "x", B = 1)) # D's dependency is not met
## [1] "Condition for 'D' not ok: A equal FALSE; instead: A=TRUE"
ps$check(list(A = TRUE, B = 1)) # B's dependency is not met
## [1] "Condition for 'B' not ok: D anyof x, y; instead: D=<not-there>"
Internally, the dependencies are represented as a data.table
, which can be accessed listed in the $deps
slot.
This data.table
can even be mutated, to e.g. remove dependencies.
There are no sanity checks done when the $deps
slot is changed this way.
Therefore it is advised to be cautious.
5.4.2.3 Vector Parameters
Unlike in the old ParamHelpers
package, there are no more vectorial parameters in paradox
.
Instead, it is now possible to create multiple copies of a single parameter using the $rep
function.
This creates a ParamSet
consisting of multiple copies of the parameter, which can then (optionally) be added to another ParamSet
.
ps2d = ParamDbl$new("x", lower = 0, upper = 1)$rep(2)
print(ps2d)
## ParamSet:
## id class lower upper levels default value
## 1: x_rep_1 ParamDbl 0 1 <NoDefault>
## 2: x_rep_2 ParamDbl 0 1 <NoDefault>
ps$add(ps2d)
print(ps)
## ParamSet:
## id class lower upper levels default parents value
## 1: A ParamLgl NA NA TRUE,FALSE <NoDefault> TRUE
## 2: B ParamInt 0 10 <NoDefault> D 1
## 3: C ParamDbl 0 4 <NoDefault>
## 4: D ParamFct NA NA x,y,z y A
## 5: E ParamUty NA NA <NoDefault>
## 6: x_rep_1 ParamDbl 0 1 <NoDefault>
## 7: x_rep_2 ParamDbl 0 1 <NoDefault>
It is also possible to use a ParamUty
to accept vectorial parameters, which also works for parameters of variable length.
A ParamSet
containing a ParamUty
can be used for parameter checking, but not for sampling.
To sample values for a method that needs a vectorial parameter, it is advised to use a parameter transformation function that creates a vector from atomic values.
Assembling a vector from repeated parameters is aided by the parameter’s $tags
: Parameters that were generated by the $rep()
command automatically get tagged as belonging to a group of repeated parameters.
5.4.3 Parameter Sampling
It is often useful to have a list of possible parameter values that can be systematically iterated through, for example to find parameter values for which an algorithm performs particularly well (tuning).
paradox
offers a variety of functions that allow creating evenly-spaced parameter values in a “grid” design as well as random sampling.
In the latter case, it is possible to influence the sampling distribution in more or less fine detail.
A point to always keep in mind while sampling is that only numerical and factorial parameters that are bounded can be sampled from, i.e. not ParamUty
.
Furthermore, for most samplers ParamInt
and ParamDbl
must have finite lower and upper bounds.
5.4.3.1 Parameter Designs
Functions that sample the parameter space fundamentally return an object of the Design
class.
These objects contain the sampled data as a data.table
under the $data
slot, and also offer conversion to a list of parameter-values using the $transpose()
function.
5.4.3.2 Grid Design
The generate_design_grid()
function is used to create grid designs that contain all combinations of parameter values: All possible values for ParamLgl
and ParamFct
, and values with a given resolution for ParamInt
and ParamDbl
.
The resolution can be given for all numeric parameters, or for specific named parameters through the param_resolutions
parameter.
5.4.3.3 Random Sampling
paradox
offers different methods for random sampling, which vary in the degree to which they can be configured.
The easiest way to get a uniformly random sample of parameters is generate_design_random
.
It is also possible to create “latin hypercube” sampled parameter values using generate_design_lhs
, which utilizes the lhs package.
LHS-sampling creates low-discrepancy sampled values that cover the parameter space more evenly than purely random values.
5.4.3.4 Generalized Sampling: The Sampler
Class
It may sometimes be desirable to configure parameter sampling in more detail.
paradox
uses the Sampler
abstract base class for sampling, which has many different sub-classes that can be parameterized and combined to control the sampling process.
It is even possible to create further sub-classes of the Sampler
class (or of any of its subclasses) for even more possibilities.
Every Sampler
object has a sample()
function, which takes one argument, the number of instances to sample, and returns a Design
object.
5.4.3.4.1 1D-Samplers
There is a variety of samplers that sample values for a single parameter.
These are Sampler1DUnif
(uniform sampling), Sampler1DCateg
(sampling for categorical parameters), Sampler1DNormal
(normally distributed sampling, truncated at parameter bounds), and Sampler1DRfun
(arbitrary 1D sampling, given a random-function).
These are initialized with a single Param
, and can then be used to sample values.
5.4.3.4.2 Hierarchical Sampler
The SamplerHierarchical
sampler is an auxiliary sampler that combines many 1D-Samplers to get a combined distribution.
Its name “hierarchical” implies that it is able to respect parameter dependencies.
This suggests that parameters only get sampled when their dependencies are met.
The following example shows how this works: The Int
parameter B
depends on the Lgl
parameter A
being TRUE
.
A
is sampled to be TRUE
in about half the cases, in which case B
takes a value between 0 and 10.
In the cases where A
is FALSE
, B
is set to NA
.
psSmall$add_dep("B", "A", CondEqual$new(TRUE))
sampH = SamplerHierarchical$new(psSmall,
list(Sampler1DCateg$new(parA),
Sampler1DUnif$new(parB),
Sampler1DUnif$new(parC))
)
sampled = sampH$sample(1000)
table(sampled$data[, c("A", "B")], useNA = "ifany")
## B
## A 0 1 2 3 4 5 6 7 8 9 10 <NA>
## FALSE 0 0 0 0 0 0 0 0 0 0 0 499
## TRUE 40 47 44 50 47 41 52 52 35 40 53 0
5.4.3.4.3 Joint Sampler
Another way of combining samplers is the SamplerJointIndep
.
SamplerJointIndep
also makes it possible to combine Sampler
s that are not 1D.
However, SamplerJointIndep
currently can not handle ParamSet
s with dependencies.
5.4.3.4.4 SamplerUnif
The Sampler
used in generate_design_random
is the SamplerUnif
sampler, which corresponds to a HierarchicalSampler
of Sampler1DUnif
for all parameters.
5.4.4 Parameter Transformation
While the different Sampler
s allow for a wide specification of parameter distributions, there are cases where the simplest way of getting a desired distribution is to sample parameters from a simple distribution (such as the uniform distribution) and then transform them.
This can be done by assigning a function to the $trafo
slot of a ParamSet
.
The $trafo
function is called with two parameters:
- The list of parameter values to be transformed as
x
- The
ParamSet
itself asparam_set
The $trafo
function must return a list of transformed parameter values.
The transformation is performed when calling the $transpose
function of the Design
object returned by a Sampler
with the trafo
ParamSet to TRUE
(the default).
The following, for example, creates a parameter that is exponentially distributed:
psexp = ParamSet$new(list(ParamDbl$new("par", 0, 1)))
psexp$trafo = function(x, param_set) {
x$par = -log(x$par)
x
}
design = generate_design_random(psexp, 2)
print(design)
## <Design> with 2 rows:
## par
## 1: 0.1314
## 2: 0.4674
design$transpose() # trafo is TRUE
## [[1]]
## [[1]]$par
## [1] 2.029
##
##
## [[2]]
## [[2]]$par
## [1] 0.7606
Compare this to $transpose()
without transformation:
design$transpose(trafo = FALSE)
## [[1]]
## [[1]]$par
## [1] 0.1314
##
##
## [[2]]
## [[2]]$par
## [1] 0.4674
5.4.4.1 Transformation between Types
Usually the design created with one ParamSet
is then used to configure other objects that themselves have a ParamSet
which defines the values they take.
The ParamSet
s which can be used for random sampling, however, are restricted in some ways:
They must have finite bounds, and they may not contain “untyped” (ParamUty
) parameters.
$trafo
provides the glue for these situations.
There is relatively little constraint on the trafo function’s return value, so it is possible to return values that have different bounds or even types than the original ParamSet
.
It is even possible to remove some parameters and add new ones.
Suppose, for example, that a certain method requires a function as a parameter.
Let’s say a function that summarizes its data in a certain way.
The user can pass functions like median()
or mean()
, but could also pass quantiles or something completely different.
This method would probably use the following ParamSet
:
methodPS = ParamSet$new(
list(
ParamUty$new("fun",
custom_check = function(x) checkmate::checkFunction(x, nargs = 1))
)
)
print(methodPS)
## ParamSet:
## id class lower upper levels default value
## 1: fun ParamUty NA NA <NoDefault>
If one wanted to sample this method, using one of four functions, a way to do this would be:
samplingPS = ParamSet$new(
list(
ParamFct$new("fun", c("mean", "median", "min", "max"))
)
)
samplingPS$trafo = function(x, param_set) {
# x$fun is a `character(1)`,
# in particular one of 'mean', 'median', 'min', 'max'.
# We want to turn it into a function!
x$fun = get(x$fun, mode = "function")
x
}
design = generate_design_random(samplingPS, 2)
print(design)
## <Design> with 2 rows:
## fun
## 1: min
## 2: median
Note that the Design
only contains the column “fun
” as a character
column.
To get a single value as a function, the $transpose
function is used.
xvals = design$transpose()
print(xvals[[1]])
## $fun
## function (..., na.rm = FALSE) .Primitive("min")
We can now check that it fits the requirements set by methodPS
, and that fun
it is in fact a function:
Imagine now that a different kind of parametrization of the function is desired:
The user wants to give a function that selects a certain quantile, where the quantile is set by a parameter.
In that case the $transpose
function could generate a function in a different way.
For interpretability, the parameter is called “quantile
” before transformation, and the “fun
” parameter is generated on the fly.
samplingPS2 = ParamSet$new(
list(
ParamDbl$new("quantile", 0, 1)
)
)
samplingPS2$trafo = function(x, param_set) {
# x$quantile is a `numeric(1)` between 0 and 1.
# We want to turn it into a function!
list(fun = function(input) quantile(input, x$quantile))
}
design = generate_design_random(samplingPS2, 2)
print(design)
## <Design> with 2 rows:
## quantile
## 1: 0.4332
## 2: 0.7023
The Design
now contains the column “quantile
” that will be used by the $transpose
function to create the fun
parameter.
We also check that it fits the requirement set by methodPS
, and that it is a function.
Although the name is suggestive of a “Set”-valued
Param
, this is unrelated to the other objects that follow theParamXxx
naming scheme.↩︎