# Sequential Single-Objective Bayesian Optimization

Source:`R/bayesopt_ego.R`

`mlr_loop_functions_ego.Rd`

Loop function for sequential single-objective Bayesian Optimization. Normally used inside an OptimizerMbo.

In each iteration after the initial design, the surrogate and acquisition function are updated and the next candidate is chosen based on optimizing the acquisition function.

## Usage

```
bayesopt_ego(
instance,
surrogate,
acq_function,
acq_optimizer,
init_design_size = NULL,
random_interleave_iter = 0L
)
```

## Arguments

- instance
(bbotk::OptimInstanceSingleCrit)

The bbotk::OptimInstanceSingleCrit to be optimized.- surrogate
(Surrogate)

Surrogate to be used as a surrogate. Typically a SurrogateLearner.- acq_function
(AcqFunction)

AcqFunction to be used as acquisition function.- acq_optimizer
(AcqOptimizer)

AcqOptimizer to be used as acquisition function optimizer.- init_design_size
(

`NULL`

|`integer(1)`

)

Size of the initial design. If`NULL`

and the bbotk::Archive contains no evaluations,`4 * d`

is used with`d`

being the dimensionality of the search space. Points are generated via a Sobol sequence.- random_interleave_iter
(

`integer(1)`

)

Every`random_interleave_iter`

iteration (starting after the initial design), a point is sampled uniformly at random and evaluated (instead of a model based proposal). For example, if`random_interleave_iter = 2`

, random interleaving is performed in the second, fourth, sixth, ... iteration. Default is`0`

, i.e., no random interleaving is performed at all.

## Note

The

`acq_function$surrogate`

, even if already populated, will always be overwritten by the`surrogate`

.The

`acq_optimizer$acq_function`

, even if already populated, will always be overwritten by`acq_function`

.The

`surrogate$archive`

, even if already populated, will always be overwritten by the bbotk::Archive of the bbotk::OptimInstanceSingleCrit.

## 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.Snoek, Jasper, Larochelle, Hugo, Adams, P R (2012). “Practical Bayesian Optimization of Machine Learning Algorithms.” In Pereira F, Burges CJC, Bottou L, Weinberger KQ (eds.),

*Advances in Neural Information Processing Systems*, volume 25, 2951--2959.

## Examples

```
# \donttest{
if (requireNamespace("mlr3learners") &
requireNamespace("DiceKriging") &
requireNamespace("rgenoud")) {
library(bbotk)
library(paradox)
library(mlr3learners)
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)
# expected improvement per second example
fun = function(xs) {
list(y = xs$x ^ 2, time = abs(xs$x))
}
domain = ps(x = p_dbl(lower = -10, upper = 10))
codomain = ps(y = p_dbl(tags = "minimize"), time = p_dbl(tags = "time"))
objective = ObjectiveRFun$new(fun = fun, domain = domain, codomain = codomain)
instance = OptimInstanceSingleCrit$new(
objective = objective,
terminator = trm("evals", n_evals = 5))
surrogate = default_surrogate(instance, n_learner = 2)
surrogate$cols_y = c("y", "time")
optimizer = opt("mbo",
loop_function = bayesopt_ego,
surrogate = surrogate,
acq_function = acqf("eips"),
acq_optimizer = acq_optimizer)
optimizer$optimize(instance)
}
#> x x_domain y
#> <num> <list> <num>
#> 1: 0.5609628 <list[1]> 0.3146792
# }
```