Acquisition Function Stochastic Expected Improvement

Expected Improvement with epsilon decay. \(\epsilon\) is updated after each update by the formula epsilon * exp(-rate * (t %% period)) where t is the number of times the acquisition function has been updated.

While this acquisition function usually would be used within an asynchronous optimizer, e.g., OptimizerAsyncMbo, it can in principle also be used in synchronous optimizers, e.g., OptimizerMbo.

Dictionary

This AcqFunction can be instantiated via the dictionary mlr_acqfunctions or with the associated sugar function acqf():

mlr_acqfunctions$get("stochastic_ei")
acqf("stochastic_ei")

Parameters

• "epsilon" (numeric(1))
  \(\epsilon\) value used to determine the amount of exploration. Higher values result in the importance of improvements predicted by the posterior mean decreasing relative to the importance of potential improvements in regions of high predictive uncertainty. Defaults to 0.1.

• "rate" (numeric(1))
  Defaults to 0.05.

• "period" (integer(1))
  Period of the exponential decay. Defaults to NULL, i.e., the decay has no period.

Note

• This acquisition function always also returns its current (acq_epsilon) and original (acq_epsilon_0) \(\epsilon\). These values will be logged into the bbotk::ArchiveBatch of the bbotk::OptimInstanceBatch of the AcqOptimizer and therefore also in the bbotk::Archive of the actual bbotk::OptimInstance that is to be optimized.

References

• Jones, R. D, Schonlau, Matthias, Welch, J. W (1998). “Efficient Global Optimization of Expensive Black-Box Functions.” Journal of Global optimization, 13(4), 455–492.

See also

Other Acquisition Function: AcqFunction, mlr_acqfunctions, mlr_acqfunctions_aei, mlr_acqfunctions_cb, mlr_acqfunctions_ehvi, mlr_acqfunctions_ehvigh, mlr_acqfunctions_ei, mlr_acqfunctions_eips, mlr_acqfunctions_mean, mlr_acqfunctions_multi, mlr_acqfunctions_pi, mlr_acqfunctions_sd, mlr_acqfunctions_smsego, mlr_acqfunctions_stochastic_cb

Super classes

bbotk::Objective -> mlr3mbo::AcqFunction -> AcqFunctionStochasticEI

Public fields

y_best

(numeric(1))
Best objective function value observed so far. In the case of maximization, this already includes the necessary change of sign.

Methods

Public methods

• AcqFunctionStochasticEI$new()

• AcqFunctionStochasticEI$update()

• AcqFunctionStochasticEI$reset()

• AcqFunctionStochasticEI$clone()

Inherited methods

• bbotk::Objective$eval()
• bbotk::Objective$format()
• bbotk::Objective$help()
• bbotk::Objective$print()
• mlr3mbo::AcqFunction$eval_dt()
• mlr3mbo::AcqFunction$eval_many()

---

Method new()

Creates a new instance of this R6 class.

Usage

AcqFunctionStochasticEI$new(
  surrogate = NULL,
  epsilon = 0.1,
  rate = 0.05,
  period = NULL
)

Arguments

surrogate

(NULL | SurrogateLearner).

epsilon

(numeric(1)).

rate

(numeric(1)).

period

(NULL | integer(1)).

---

Method update()

Update the acquisition function. Sets y_best to the best observed objective function value. Decays epsilon.

Usage

AcqFunctionStochasticEI$update()

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Method reset()

Reset the acquisition function. Resets the private update counter .t used within the epsilon decay.

Usage

AcqFunctionStochasticEI$reset()

---

Method clone()

The objects of this class are cloneable with this method.

Usage

AcqFunctionStochasticEI$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

if (requireNamespace("mlr3learners") &
    requireNamespace("DiceKriging") &
    requireNamespace("rgenoud")) {
  library(bbotk)
  library(paradox)
  library(mlr3learners)
  library(data.table)

  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 = OptimInstanceBatchSingleCrit$new(
    objective = objective,
    terminator = trm("evals", n_evals = 5))

  instance$eval_batch(data.table(x = c(-6, -5, 3, 9)))

  learner = default_gp()

  surrogate = srlrn(learner, archive = instance$archive)

  acq_function = acqf("stochastic_ei", surrogate = surrogate)

  acq_function$surrogate$update()
  acq_function$update()
  acq_function$eval_dt(data.table(x = c(-1, 0, 1)))
}
#>      acq_ei acq_epsilon acq_epsilon_0
#>       <num>       <num>         <num>
#> 1: 4.374607         0.1           0.1
#> 2: 4.835292         0.1           0.1
#> 3: 5.262107         0.1           0.1