mlr_optimizers_hyperband: Optimizer Using the Hyperband Algorithm

In mlr3hyperband: Hyperband for 'mlr3'

Optimizer Using the Hyperband Algorithm

Description

Optimizer using the Hyperband (HB) algorithm. HB runs the Successive Halving Algorithm (SHA) with different numbers of stating configurations. The algorithm is initialized with the same parameters as Successive Halving but without n. Each run of Successive Halving is called a bracket and starts with a different budget r_0. A smaller starting budget means that more configurations can be tried out. The most explorative bracket allocated the minimum budget r_min. The next bracket increases the starting budget by a factor of eta. In each bracket, the starting budget increases further until the last bracket s = 0 essentially performs a random search with the full budget r_max. The number of brackets s_max + 1 is calculated with s_max = log(r_min / r_max)(eta). Under the condition that r_0 increases by eta with each bracket, r_min sometimes has to be adjusted slightly in order not to use more than r_max resources in the last bracket. The number of configurations in the base stages is calculated so that each bracket uses approximately the same amount of budget. The following table shows a full run of HB with eta = 2, r_min = 1 and r_max = 8.

s			3			2			1			0
i		n_i	r_i		n_i	r_i		n_i	r_i		n_i	r_i
0		8	1		6	2		4	4		8	4
1		4	2		3	4		2	8
2		2	4		1	8
3		1	8

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

The budget hyperparameter must be tagged with "budget" in the search space. The minimum budget (r_min) which is allocated in the base stage of the most explorative bracket, is set by the lower bound of the budget parameter. The upper bound defines the maximum budget (r_max) which is allocated to the candidates in the last stages.

Resources

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

• Tune the hyperparameters of XGBoost with Hyperband.

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

Dictionary

This Optimizer can be instantiated via the dictionary mlr_optimizers or with the associated sugar function opt():

mlr_optimizers$get("hyperband")
opt("hyperband")

Parameters

eta

numeric(1)
With every stage, the budget is increased by a factor of eta and only the best 1 / eta points 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 in the base stage of each bracket. The default is uniform sampling.

repetitions

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

Archive

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

• bracket (integer(1))
  The bracket index. Counts down to 0.

• stage (integer(1))
  The stages of each bracket. Starts counting at 0.

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

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 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").

Logging

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

Super class

bbotk::Optimizer -> OptimizerHyperband

Methods

Public methods

• OptimizerHyperband$new()

• OptimizerHyperband$clone()

Inherited methods

• bbotk::Optimizer$format()
• bbotk::Optimizer$help()
• bbotk::Optimizer$optimize()
• bbotk::Optimizer$print()

---

Method new()

Creates a new instance of this R6 class.

Usage

OptimizerHyperband$new()

---

Method clone()

The objects of this class are cloneable with this method.

Usage

OptimizerHyperband$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Source

Li L, Jamieson K, DeSalvo G, Rostamizadeh A, Talwalkar A (2018). “Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization.” Journal of Machine Learning Research, 18(185), 1-52. https://jmlr.org/papers/v18/16-558.html.

Examples

library(bbotk)
library(data.table)

# set search space
search_space = domain = ps(
  x1 = p_dbl(-5, 10),
  x2 = p_dbl(0, 15),
  fidelity = p_dbl(1e-2, 1, tags = "budget")
)

# Branin function with fidelity, see `bbotk::branin()`
fun = function(xs) branin_wu(xs[["x1"]], xs[["x2"]], xs[["fidelity"]])

# create objective
objective = ObjectiveRFun$new(
  fun = fun,
  domain = domain,
  codomain = ps(y = p_dbl(tags = "minimize"))
)

# initialize instance and optimizer
instance = OptimInstanceSingleCrit$new(
  objective = objective,
  search_space = search_space,
  terminator = trm("evals", n_evals = 50)
)

optimizer = opt("hyperband")

# optimize branin function
optimizer$optimize(instance)

# best scoring evaluation
instance$result

# all evaluations
as.data.table(instance$archive)

mlr3hyperband documentation built on March 7, 2023, 5:18 p.m.