Flexible Bayesian Optimization

A modern and flexible approach to Bayesian Optimization / Model Based Optimization building on the 'bbotk' package. 'mlr3mbo' is a toolbox providing both ready-to-use optimization algorithms as well as their fundamental building blocks allowing for straightforward implementation of custom algorithms. Single- and multi-objective optimization is supported as well as mixed continuous, categorical and conditional search spaces. Moreover, using 'mlr3mbo' for hyperparameter optimization of machine learning models within the 'mlr3' ecosystem is straightforward via 'mlr3tuning'. Examples of ready-to-use optimization algorithms include Efficient Global Optimization by Jones et al. (1998) , ParEGO by Knowles (2006) and SMS-EGO by Ponweiser et al. (2008) .

mlr3mbo

Package website: release | dev

A new R6 and much more modular implementation for single- and multi-objective Bayesian Optimization.

Get Started

The best entry point to get familiar with mlr3mbo is provided via the Bayesian Optimization chapter in the mlr3book.

Design

mlr3mbo is built modular relying on the following R6 classes:

• Surrogate: Surrogate Model
• AcqFunction: Acquisition Function
• AcqOptimizer: Acquisition Function Optimizer

Based on these, Bayesian Optimization (BO) loops can be written, see, e.g., bayesopt_ego for sequential single-objective BO.

mlr3mbo also provides an OptimizerMbo class behaving like any other Optimizer from the bbotk package as well as a TunerMbo class behaving like any other Tuner from the mlr3tuning package.

mlr3mbo uses sensible defaults for the Surrogate, AcqFunction, AcqOptimizer, and the loop_function. See mbo_defaults for more details on all defaults.

Simple Optimization Example

Minimize the two-dimensional Branin function via sequential BO using a GP as surrogate and EI as acquisition function optimized via a local search:

library(bbotk)
library(mlr3mbo)
library(mlr3learners)
set.seed(1)

fun = function(xdt) {
  y = branin(xdt[["x1"]], xdt[["x2"]])
  data.table(y = y)
}

domain = ps(
  x1 = p_dbl(-5, 10),
  x2 = p_dbl(0, 15)
)

codomain = ps(
  y = p_dbl(tags = "minimize")
)

objective = ObjectiveRFunDt$new(
  fun = fun,
  domain = domain,
  codomain = codomain
)

instance = oi(
  objective = objective,
  terminator = trm("evals", n_evals = 25)
)

surrogate = srlrn(lrn("regr.km", control = list(trace = FALSE)))

acq_function = acqf("ei")

acq_optimizer = acqo("local_search", n_searches = 10, n_steps = 5, n_neighs = 10)

optimizer = opt("mbo",
  loop_function = bayesopt_ego,
  surrogate = surrogate,
  acq_function = acq_function,
  acq_optimizer = acq_optimizer
)

optimizer$optimize(instance)

##           x1       x2  x_domain         y
##        <num>    <num>    <list>     <num>
## 1: -3.152173 12.30826 <list[2]> 0.3984859

We can quickly visualize the contours of the objective function (on log scale) as well as the sampling behavior of our BO run (lighter blue colors indicating points that were evaluated in later stages of the optimization process; the first batch is given by the initial design).

library(ggplot2)
grid = generate_design_grid(instance$search_space, resolution = 1000L)$data
grid[, y := branin(x1 = x1, x2 = x2)]

ggplot(aes(x = x1, y = x2, z = log(y)), data = grid) +
  geom_contour(color = "black") +
  geom_point(aes(x = x1, y = x2, color = batch_nr), data = instance$archive$data) +
  labs(x =  expression(x[1]), y = expression(x[2])) +
  theme_minimal() +
  theme(legend.position = "bottom")

Note that you can also use bb_optimize as a shorthand instead of constructing an optimization instance.

Simple Tuning Example

library(mlr3)
library(mlr3learners)
library(mlr3tuning)
library(mlr3mbo)
set.seed(1)

task = tsk("sonar")

learner = lrn("classif.rpart", cp = to_tune(lower = 1e-04, upper = 1, logscale = TRUE))

instance = tune(
  tuner = tnr("mbo"),
  task = task,
  learner = learner,
  resampling = rsmp("holdout"),
  measure = msr("classif.ce"),
  term_evals = 10)

instance$result

##           cp learner_param_vals  x_domain classif.ce
##        <num>             <list>    <list>      <num>
## 1: -6.220556          <list[2]> <list[1]>  0.2382812

Citation

If you use mlr3mbo, please cite our paper.

Becker M, Schneider L, Binder M, Kotthoff L, Bischl B (2026). “mlr3mbo: Bayesian Optimization in R.” Patterns. https://doi.org/10.1016/j.patter.2026.101614.

@Article{becker2026mlr3mbo,
  title = {mlr3mbo: Bayesian Optimization in R},
  author = {Marc Becker and Lennart Schneider and Martin Binder and Lars Kotthoff and Bernd Bischl},
  year = {2026},
  journal = {Patterns},
  doi = {10.1016/j.patter.2026.101614},
  url = {https://doi.org/10.1016/j.patter.2026.101614},
}