Hyperparameter Tuning with Successive Halving

Optimizer using the Successive Halving Algorithm (SHA). SHA is initialized with the number of starting configurations n, the proportion of configurations discarded in each stage eta, and the minimum r_min and maximum _max budget of a single evaluation. The algorithm starts by sampling n random configurations and allocating the minimum budget r_min to them. The configurations are evaluated and 1 / eta of the worst-performing configurations are discarded. The remaining configurations are promoted to the next stage and evaluated on a larger budget. The following table is the stage layout for eta = 2, r_min = 1 and r_max = 8.

i	n_i	r_i
0	8	1
1	4	2
2	2	4
3	1	8

i is the stage number, n_i is the number of configurations and r_i is the budget allocated to a single configuration.

The number of stages is calculated so that each stage consumes approximately the same budget. This sometimes results in the minimum budget having to be slightly adjusted by the algorithm.

Source

Jamieson K, Talwalkar A (2016). “Non-stochastic Best Arm Identification and Hyperparameter Optimization.” In Gretton A, Robert CC (eds.), Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, volume 51 series Proceedings of Machine Learning Research, 240-248. http://proceedings.mlr.press/v51/jamieson16.html.

Dictionary

This mlr3tuning::Tuner can be instantiated via the dictionary mlr3tuning::mlr_tuners or with the associated sugar function mlr3tuning::tnr():

TunerBatchSuccessiveHalving$new()
mlr_tuners$get("successive_halving")
tnr("successive_halving")

Subsample Budget

If the learner lacks a natural budget parameter, mlr3pipelines::PipeOpSubsample can be applied to use the subsampling rate as budget parameter. The resulting mlr3pipelines::GraphLearner is fitted on small proportions of the mlr3::Task in the first stage, and on the complete task in last stage.

Custom Sampler

Hyperband supports custom paradox::Sampler object for initial configurations in each bracket. A custom sampler may look like this (the full example is given in the examples section):

# - beta distribution with alpha = 2 and beta = 5
# - categorical distribution with custom probabilities
sampler = SamplerJointIndep$new(list(
  Sampler1DRfun$new(params[[2]], function(n) rbeta(n, 2, 5)),
  Sampler1DCateg$new(params[[3]], prob = c(0.2, 0.3, 0.5))
))

Progress Bars

$optimize() supports progress bars via the package progressr combined with a bbotk::Terminator. Simply wrap the function in progressr::with_progress() to enable them. We recommend to use package progress as backend; enable with progressr::handlers("progress").

Parallelization

The hyperparameter configurations of one stage are evaluated in parallel with the future package. To select a parallel backend, use the plan() function of the future package.

Logging

Hyperband uses a logger (as implemented in lgr) from package bbotk. Use lgr::get_logger("bbotk") to access and control the logger.

Resources

The gallery features a collection of case studies and demos about optimization.

• Tune the hyperparameters of XGBoost with Hyperband (Hyperband can be easily swapped with SHA).

• Use data subsampling and Hyperband to optimize a support vector machine.

Parameters

n

integer(1)
Number of configurations in the base stage.

eta

numeric(1)
With every stage, the budget is increased by a factor of eta and only the best 1 / eta configurations are promoted to the next stage. Non-integer values are supported, but eta is not allowed to be less or equal to 1.

sampler

paradox::Sampler
Object defining how the samples of the parameter space should be drawn. The default is uniform sampling.

repetitions

integer(1)
If 1 (default), optimization is stopped once all stages are evaluated. Otherwise, optimization is stopped after repetitions runs of SHA. The bbotk::Terminator might stop the optimization before all repetitions are executed.

adjust_minimum_budget

logical(1)
If TRUE, the minimum budget is increased so that the last stage uses the maximum budget defined in the search space.

Archive

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

• stage (integer(1))
  Stage index. Starts counting at 0.

• repetition (integer(1))
  Repetition index. Start counting at 1.

Super classes

mlr3tuning::Tuner -> mlr3tuning::TunerBatch -> mlr3tuning::TunerBatchFromOptimizerBatch -> TunerBatchSuccessiveHalving

Methods

Public methods

• TunerBatchSuccessiveHalving$new()

• TunerBatchSuccessiveHalving$clone()

Inherited methods

• mlr3tuning::Tuner$format()
• mlr3tuning::Tuner$help()
• mlr3tuning::Tuner$print()
• mlr3tuning::TunerBatchFromOptimizerBatch$optimize()

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Method new()

Creates a new instance of this R6 class.

Usage

TunerBatchSuccessiveHalving$new()

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Method clone()

The objects of this class are cloneable with this method.

Usage

TunerBatchSuccessiveHalving$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

if(requireNamespace("xgboost")) {
  library(mlr3learners)

  # define hyperparameter and budget parameter
  search_space = ps(
    nrounds = p_int(lower = 1, upper = 16, tags = "budget"),
    eta = p_dbl(lower = 0, upper = 1),
    booster = p_fct(levels = c("gbtree", "gblinear", "dart"))
  )

  # \donttest{
  # hyperparameter tuning on the pima indians diabetes data set
  instance = tune(
    tnr("successive_halving"),
    task = tsk("pima"),
    learner = lrn("classif.xgboost", eval_metric = "logloss"),
    resampling = rsmp("cv", folds = 3),
    measures = msr("classif.ce"),
    search_space = search_space,
    term_evals = 100
  )

  # best performing hyperparameter configuration
  instance$result
  # }
}
#>    nrounds       eta booster learner_param_vals  x_domain classif.ce
#>      <num>     <num>  <char>             <list>    <list>      <num>
#> 1:       2 0.7313306    dart          <list[6]> <list[3]>  0.2473958