[dask] Support custom metric functions

[jameslamb]

Summary

The Dask estimators in lightgbm.dask should support the use of a custom objective function.

Motivation

Defining custom metrics functions gives users fine-grained ability to evaluate what's happening during training, and to control the training process via early stopping (#3712).

This feature would also bring Dask estimators closer to parity with the sklearn estimators.

Description

I haven't thought through this much yet, just writing up a placeholder issue for discussion. If you're reading this and have ideas, please comment and the issue can be re-opened.

References

See LINK for an explanation of how this works in the sklearn estimators.

Can look at how xgboost.dask handles this for inspiration:

• https://github.com/dmlc/xgboost/blob/4c5d2608e0bd179bfc5a8e9b3132e6651f841256/python-package/xgboost/dask.py#L1565
• https://github.com/dmlc/xgboost/blob/4c5d2608e0bd179bfc5a8e9b3132e6651f841256/python-package/xgboost/dask.py#L1838-L1841
• https://github.com/dmlc/xgboost/blob/4c5d2608e0bd179bfc5a8e9b3132e6651f841256/python-package/xgboost/dask.py#L850

At a quick glance it seems like xgboost.dask just passes the function all the way through to training and it "just works". Maybe we'll get lucky 😂

[jameslamb]

Closing this in favor of putting it in #2302 with other feature requests. Please comment if you're interested in working on this and the issue can be re-opened.

[jameslamb]

Re-opening this. I think it can be closed by a pull request that is currently in progress: #4101 (comment)

[jameslamb]

fixed by #4101, thanks @ffineis !