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using the "Write to Database", I mange to save all my prediction results into SQL.
In addition, I want to add data to SQL that details the model parameters that have generated the predicitions, such as which loss function or how many trees have been used - is there an easy way to do so in RM ?
Anything you can convert into an example set you can put into a database. The Converters extension contains some operators for that.
You could also use Log to Data if you have a complex optimization process and save the different parameters with the performance you achieved in the database.