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* Turn `early_stopping` into a Callable class

* Fix

* Lint

* Remove print

* Fix order

* Revert "Lint"

This reverts commit 7ca8b557572446888cf793c0082d9a7efd1e29a7.

* Apply suggestion from code review

* Nit

* Lint

* Move callable class outside the func for pickling

* Move _pickle and _unpickle to tests utils

* Add early stopping callback picklability test

* Nit

* Fix

* Lint

* Improve type hint

* Lint

* Lint

* Add cloudpickle to test_windows

* Update tests/python_package_test/test_engine.py

* Fix

* Apply suggestions from code review