Description
It would be useful to have some mechanism of determining supported solvers for a given estimator. First, because currently check_estimator only runs on the default solver and so we are potentially not testing a number of configurations.
It would also make easier to check that all solvers yield comparable results such as #13914
Of course, this can also be generalized to other parameters that impact the solver but should not change the way estimator behaves.
One way could be just to store e.g. _supported_solvers as a private attribute, or possibly in type annotations (though this would require PEP 586 from Python 3.8 that can be backported by vendoring typing_extensions.py), related to #11170
Another way could be to have some method that yields possible estimator variants to be tested. @amueller if I remember correctly you mentioned something similar in the estimator tags PR.