mlr3 optimized average of ensemble

Question

I try to optimize the averaged prediction of two logistic regressions in a classification task using a superlearner.

My measure of interest is classif.auc

The mlr3 help file tells me (?mlr_learners_avg)

Predictions are averaged using weights (in order of appearance in the data) which are optimized using nonlinear optimization from the package "nloptr" for a measure provided in measure (defaults to classif.acc for LearnerClassifAvg and regr.mse for LearnerRegrAvg). Learned weights can be obtained from $model. Using non-linear optimization is implemented in the SuperLearner R package. For a more detailed analysis the reader is referred to LeDell (2015).

I have two questions regarding this information:

1. When I look at the source code I think LearnerClassifAvg$new() defaults to "classif.ce", is that true? I think I could set it to classif.auc with param_set$values <- list(measure="classif.auc",optimizer="nloptr",log_level="warn")

2. The help file refers to the SuperLearner package and LeDell 2015. As I understand it correctly, the proposed "AUC-Maximizing Ensembles through Metalearning" solution from the paper above is, however, not impelemented in mlr3? Or do I miss something? Could this solution be applied in mlr3? In the mlr3 book I found a paragraph regarding calling an external optimization function, would that be possible for SuperLearner?

Answer 1

As far as I understand it, LeDell2015 proposes and evaluate a general strategy that optimizes AUC as a black-box function by learning optimal weights. They do not really propose a best strategy or any concrete defaults so I looked into the defaults of the SuperLearner package's AUC optimization strategy.

Assuming I understood the paper correctly:

The LearnerClassifAvg basically implements what is proposed in LeDell2015 namely, it optimizes the weights for any metric using non-linear optimization. LeDell2015 focus on the special case of optimizing AUC. As you rightly pointed out, by setting the measure to "classif.auc" you get a meta-learner that optimizes AUC. The default with respect to which optimization routine is used deviates between mlr3pipelines and the SuperLearner package, where we use NLOPT_LN_COBYLA and SuperLearner ... uses the Nelder-Mead method via the optim function to minimize rank loss (from the documentation).

So in order to get exactly the same behaviour, you would need to implement a Nelder-Mead bbotk::Optimizer similar to here that simply wraps stats::optim with method Nelder-Mead and carefully compare settings and stopping criteria. I am fairly confident that NLOPT_LN_COBYLA delivers somewhat comparable results, LeDell2015 has a comparison of the different optimizers for further reference.

Thanks for spotting the error in the documentation. I agree, that the description is a little unclear and I will try to improve this!