Thanks for the PR and sorry for the slow reply.
I think if we want to minimize MAPE using SGD we might also want to add it to the metrics module.
Would you like to do that?

Also, this needs to be added to the docstrings explaining the possible losses and needs a test that it's actually minimizing mape.

I think it's a good idea to adding MAPE as a loss function.
Actually ,I'm considering using it.
Could you please show me some examples about how to use MAPE in scikit-learning?

You could load this branch into your working copy, merge it with the current master, install it and use... It would not take a great deal of effort to get this PR to a state where it could be merged, but we won't merge it without appropriate documentation and tests. And as @amueller says, it would be good to have MAPE as an evaluation metric for symmetry.

Also needs some docs, at least mention in the docstring. Also in whatsnew. Not sure how easy it is to test this as part of SGDClassifier. Maybe hand-designed example?

Numerically, I see issues with y==0 and at the point when the derivative is undefined. Are there any references or papers for doing stochastic gradient descent with MAPE as a loss function?

@thomasjpfan this pull request was superseded by #10711, itself closed in favor of #15007. Can we close it?

This PR is a little different from #15007. #15007 adds MAPE to the metrics module, while this one is adding it as a loss to SGDRegressor.

I would still consider this a candidate for closing, unless there is a reference or paper that demonstrates the usefulness of using MAPE for SGD.