In berndbischl/mlrMBO: Bayesian Optimization and Model-Based Optimization of Expensive Black-Box Functions

Model Based Optimization

The generic sequential model-based optimization (SMBO) procedure starts with an initial design of evaluation points.

Subsequently, the following steps are performed iteratively until a termination criterion is met:

1. Fit a regression model to the design, based on the information gained from evaluating the black-box function at the points in the design
2. A new point is proposed by the surrogate model and the infill criterion.
3. Evaluate the black-box function at this point and add it to the design.

Types of MBO supported in mlrMBO

In addition to SMBO mlrMBO also supports mulit-critera optimization and parallel optimization.

Surrogate Model

The attribute learner of the mbo() function allows us to choose an appropriate surrogate model for the parameter optimization. Different learners can easily be created using the makeLearner function from the mlr package. A list of implemented learners can be seen using the listlearners() function or on the mlr wiki.

The choice of the surrogate model depends on the parameter set of the objective function. While kriging models (gaussian processes) are advisable if all parameters are numeric, they cannot be used if the objective function contains categorical parameters. If at least one parameter is categorical, random forest models might be a good choice as surrogate models. The default kriging model is from the DiceKriging package and uses the matern5_2covariance kernel.

Infill Criterion

One of the most important questions is to define how the next design points in the sequential loop are chosen. With setMBOControlInfill a MBOControl object can be extended with infill criteria and infill optimizer options.

Argument crit

5 different possibilities can be set via the crit argument in setMBOControlInfill:

• mean: mean response of the surrogate model
• ei: expected improvement of the surrogate model
• aei: augmented expected improvement, which is especially useful for noisy functions
• eqi: expected quantile improvement
• cb: confidence bound, which is the additive combination of mean response and mean standard error estimation of the surrogate model (response - lambda * standard.error)

The parameters of the different criteria are set via further arguments (e.g. crit.cb.lambds for the lambda parameter if crit = cb)

berndbischl/mlrMBO documentation built on Oct. 11, 2022, 1:44 p.m.