Is it desirable / possible to apply ensemble learning methods (boosting, bagging, etc) to the quantile regression problem?
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Yes, and in fact this has been addressed in the literature. Quantile random forests adapt the random forest framework for quantile regression and the author provides consistency proofs. There is an R package implementing the technique as well here.
In terms of desirability, ensembles will help with the bias/variance problem for quantile regression just as well as predicting the mean.
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$\begingroup$ Do you have a good primer on bias/variance tradeoffs regarding quantile regression? $\endgroup$ Commented Jun 23, 2020 at 18:34