I would like to use model-based optimization within the mlr-Package in R (mlrMBO) to tune my hyperparameters. How many iterations are recommended here? I have read that the number of necessary iterations in MBO depends on the number of hyperparameters, that should be multiplied by a certain factor?
Unfortunately there's no general answer to this. In addition to the number of hyperparameters, the difficulty of the task and the general optimization landscape have an impact on how many iterations may be needed. Furthermore, it depends on what level of performance you're looking for -- if you absolutely need the best performance, you may need a lot of iterations (thousands or more).
A good rule of thumb is to determine the number of iterations based on the resources you have available. Do you need an answer in a few minutes or can you leave it run overnight? I would start with a small test run with only a few iterations to get a feeling for how long it takes in your particular case and then set the number of iterations for a real run based on that and how long you want to spend on it.
It's also a good idea to do multiple runs with different random seeds and the same number of iterations and the same random seed and different numbers of iterations. This will tell you how much more performance you can get by running longer, e.g. if there is no difference for 100 and 1000 iterations then giving it more may not be worth it.